Chuck and Cindy Nemser have lived in a townhouse in Park Slope for 47 years. Until she began suffering from unexplained nerve pain a few years ago, Ms. Nemser, 77, an art historian and writer, would happily retreat to her third-floor office where she could work undisturbed. There’s plenty of wall space for the couple’s art collection, and ample storage for Mr. Nemser’s cache of fishing poles.

But the stairs have become increasingly difficult for Ms. Nemser to negotiate, and late this spring, Mr. Nemser, 80, an independent salesman, retired. The time was ripe to put the house on the market.

But let’s be clear: Leaving town isn’t an option. “I love the arts and I want to stay in New York,” Ms. Nemser said.

She speaks for thousands.

It used to be that New Yorkers of a certain age reflexively said goodbye to all this — the traffic, the tumult, the long lines and the incomparable bagels — and headed south or west for their sunset years. No longer. Around town these days there are many more than 50 shades of gray. According to the city’s Department for the Aging, the 60-plus population increased 12.4 percent between 2000 and 2010. By 2030 it is projected to grow by 35.3 percent to 1.84 million.

For many lucky enough in live in rent-controlled or rent-stabilized apartments, staying put makes financial sense, and may, in fact, be a financial necessity. But the elderly with sufficient resources see no good reason to clear out, either.

The Nemsers are searching for a two-bedroom rental in their neighborhood. An elevator, a garage and a doorman are all essentials. Amenities like a roof deck, a lounge or a garden are desirable “so Cindy and Chuck can begin socializing, Cindy especially,” said the couple’s sales agent, Stefania Cardinali of Citi Habitats, acknowledging that there are few properties in or around Park Slope that tick off all the boxes on the “must have” list.

For those who don’t drive, or who have trouble walking, the buses, taxis and, in some cases, free van transportation can make New York a surprisingly viable place in which to grow old. Social services and medical care are close by, in the case of the city’s 28 official NORCs (Naturally Occurring Retirement Communities), right on site. Stores and restaurants deliver. Plays, concerts, exhibitions and recitals are abundant.

But with elderly New Yorkers growing in number, landlords, resident managers and co-op boards are confronting a host of new issues, and sorting out how best to address them. While some building managers are looking for ways to accommodate aging residents, others are — for liability reasons — ordering staff to keep their distance.

“Co-op boards today are made up of a lot of a building’s younger residents,” said Harold Kobner, an associate broker at Argo Real Estate. “And the aging population in their buildings is becoming more and more of a problem because it’s a problem that has never been addressed.”

Put it down to denial. “Most people who are not of a certain age yet try to shut it out of their minds,” said Aaron Shmulewitz, a real estate lawyer at Belkin Burden Wenig & Goldman who has fielded complaints from clients about odors, hoarding and pajama-clad elderly residents wandering the halls. “They don’t want to think what it will be like when they are that age.”

Of course, residents of all ages can create headaches for the management, but these can be compounded when infirmity is part of the picture.

Steven R. Wagner, a real estate lawyer at Porzio, Bromberg & Newman, has received calls from landlords and property managers pondering what to do about a resident “who’s a shut-in or who smokes cigarettes all day long, flicks them into the fireplace, misses occasionally and starts fires,” he said, or about someone who can no longer hear and is becoming a little forgetful.

Marni J. Berk, a managing director at FirstService Residential and the general manager of Lincoln Towers, the eight-building complex on the Upper West Side, tells of the elderly resident who was washing his trousers in the sink and forgot to turn off the faucet, causing water to cascade all the way down to the lobby. Gas stoves have been left on; tenants out for a constitutional around the 20-acre property have become confused and disoriented.

One recent Saturday night at 11:30, Elaine Paris, 68, who lives in a co-op in Queens, heard the doorbell ring. There stood an elderly neighbor saying she was all alone, recalled Ms. Paris, a travel consultant who moved to the three-building complex a year ago. “I know her. She’s physically healthy and she has an aide, but she wasn’t around.”

“First I called security and he said, ‘What do you expect me to do?’ ” continued Ms. Paris, who took the woman back to her apartment, only to get another visit a half an hour later. “I walked her back home, took her to her room, turned off some lights and l literally tucked her in.”

If the neighbor had come back again, Ms. Paris said she would have called 911. “She could have fallen down a stairwell,” Ms. Paris said. “One of the guys in management said to me: ‘This is not an assisted living facility.’ It’s troublesome. It needs to be brought up to the board so there are some protocols to follow.”

Many buildings have just such protocols. “We make sure we have good contact information for the next of kin or for close friends of the elderly people who live in our buildings,” said Marina Higgins, a vice president and director of leasing for Argo Real Estate. “We also make a point of having a set of keys to the apartment of our seniors. That can be difficult,” she added. “But we try to explain to our older population that it’s in their best interest.”

The Kips Bay Towers Condominium maintains a list of elderly residents who use canes, walkers or wheelchairs or who have special needs, according to the building’s property manager, Marsha Bangaru. “And if the neighbors of a senior tell us they haven’t seen the person in a while, we’ll go up and check on the resident to make sure everything is O.K.,” she said.

Lincoln Towers, meanwhile, asks new residents, regardless of age, to fill out a form that asks questions about special needs like a walker or oxygen. “If there’s an emergency and the building needs to be evacuated, the F.D.N.Y. gets this list,” Ms. Berk said.

Often, doormen are the first line of defense. “Me and the other guys know who looks good and who doesn’t look good,” said Michael Lydon, who has been on the service staff of an Upper East Side co-op for 27 years. “We’ll say, ‘Have you seen Mrs. So-and-So recently?’ People who are elderly have a routine, like going to Gristede’s on senior citizens’ days. If they break from that routine, that makes us think we should go check on them.”

Watching a resident’s health decline can be difficult, Mr. Lydon added. “One gentleman fell a few times and I said, ‘I don’t want to be the one who comes up to find you on the floor or worse. If you’re not going to get an aide, you should at least get MedicAlert,’ ” he continued, referring to one of the many wearable alert systems.

Mr. Lydon said he doesn’t mince words because “I’ve been in the building a long time so I can talk to them a little more honestly.”

Certain buildings make special allowances and create special programs for their older residents. Technically, the community rooms at Lincoln Towers are off limits to the 10 percent of residents, all now elderly, who didn’t buy when the complex went co-op in 1987. But to accommodate events sponsored by Project Open, an on-site outreach organization for seniors, “we make an exception and donate the space,” Ms. Berk said.

Mr. Wagner represents a Brooklyn co-op with a basement laundry room. “But the elevator doesn’t go to the basement, and one elderly tenant couldn’t negotiate the stairs,” he said. So even though it was against building rules, management made an accommodation and let the resident have a washer and dryer in her apartment.

Similarly, while the Kips Bay Tower Condominium generally doesn’t permit delivery people beyond the lobby, “we let them go up to the apartments of our elderly residents,” said Ms. Bangaru, who estimates that almost half the unit owners are in their late 60s or beyond.

A committee of resident volunteers also arranges a game or bingo night in the building’s community room. “It’s been a good way to get the elderly out and socializing and meeting their neighbors,” Ms. Bangaru said. That same committee “has also put together seminars that might be beneficial to the elderly, like a technology class to teach them how to use social media to interact with their loved ones.” One class was a presentation on navigating Facebook.

Lincoln Guild Housing Corporation, an Upper West Side NORC, has an on-site outreach office that offers lectures on nutrition and estate planning, and classes in ballroom dancing, tai chi and exercise. Such programs are planned for the building’s older population (some 40 percent of the residents are over 60) but are open to all residents.

A nurse visits once a week pro bono to check the blood pressure and the medications of interested residents, according to Lucille Bruto, a social worker and director of the outreach program. Wearing medical alert devices is encouraged, “and the building gets a discount from one of the companies,” she said. The outreach office also has a fax machine, copy services and a shredder “to attract people in the building of all ages so we can make them aware of our programs,” Ms. Bruto added.

One habitué is Delos Smith. “I use the fax machine, and I have my blood pressure taken weekly. That’s very significant, because my blood pressure is right on the borderline,” said Mr. Smith, 79, a retired economist who was unaware of Lincoln Guild’s special offerings before he and his wife moved in 21 years ago. “We’d lived at 69th and Broadway and wanted a bigger apartment but wanted to stay in the area,” Mr. Smith added. “The outreach office is an insurance policy. I’m still mobile, but it’s nice to know I don’t have to move if I need more services.”

In 1997, two residents of Schwab House, a co-op on the Upper West Side, put together a 17-page “Senior Resource Directory” with the phone numbers of government agencies like the city’s Department for the Aging, as well as local pharmacies, social service agencies and senior centers in the neighborhood. “The building was very supportive and paid all the expenses of the guide,” said one of its authors, Frances Klein, 86, who’s now toying with the possibility of producing an update and who also serves on the building’s gym committee. “We have lots of equipment that’s good for seniors,” she said.

Mrs. Klein was one of many in the audience when the Schwab House Council, a volunteer group, arranged a talk by a resident, a geriatric case manager who brought along a lawyer specializing in issues relevant to the elderly. “It was mind-boggling,” Mrs. Klein recalled of the lecture, which dealt with asset management, health care proxies and living wills, among other matters. “I wouldn’t have missed it for anything.”

Meanwhile, at Morningside Heights Housing Corporation, a NORC in Upper Manhattan, “the older people want to sit out on our grounds and read a book and the younger families want their children to be able to ride a scooter,” said Russell W. Jermyn, Morningside’s general manager. “The board is restricting the size of bikes and scooters on the property and is mandating that kids can only play with balls like Nerfs or Spaldeens.”

But some buildings are leery about extending a helping hand. According to Mr. Shmulewitz, many co-op boards are issuing written orders to service staff members instructing them not to run to the aid of an elderly resident who calls to say he’s fallen and can’t get up. They are to explain that no, they can’t come upstairs to help, but yes, they will call 911.

“If the doorman goes up and lifts Mr. Smith off the floor and Mr. Smith is hurt further or expires, the co-op could incur liability,” Mr. Shmulewitz said. “If the doorman wrenches his back picking up Mr. Smith and he’s not covered by workman’s comp, once again the co-op is liable. It sounds cold and it sounds impersonal, but there’s a growing trend of these instructions.”

Liability is one concern; the impact on co-op and condo sales is another.

“People do due diligence when they’re looking to buy, and part of that is reviewing the minutes of a co-op board meeting,” said Steven D. Sladkus, a real estate lawyer at Wolf Haldenstein Adler Freeman & Herz. “If there are a lot of issues concerning elderly shareholders, like a report that there was a flood or that adult protective services was called, that might raise antennas.”

Similarly off-putting, according to Mr. Shmulewitz: an elderly pajama-clad resident camped out in the lobby. “If a real estate agent comes in with a client,” he said, “and the first thing they see is a senior in a nightgown, guess what? The apartment isn’t selling that day, at least not for the price the shareholder wants.”

In fact, many buildings have rules forbidding residents, senior or junior, regardless of their wardrobe choices, to use the lobby as anything more than a space to walk through.

Seniors? Bring them on, said Dean Feldman, an associate broker at Halstead Property and a resident of Schwab House. “I know that co-ops aren’t social service agencies,” he said. “But we can all do a lot to support all the elderly people in our buildings.” This could include designating “floor captains” who would take note of newspapers piling up in front of a door and of mail uncollected.

For his part, Mr. Feldman, 52, routinely takes an elderly neighbor to dinner, checks in with another several times a week, and does grocery shopping for yet another. “As a single person who lives alone,” he said, “I like to think I’m paying it forward.”