When Audrey Davison met someone special at her nursing home, she wanted to love her man.

Her nurses and aides at the Hebrew Home at Riverdale did not try to stop her. On the contrary, she was allowed to stay over in her boyfriend’s room with the door shut under the Bronx home’s stated “sexual expression policy.” One aide even made the couple a “Do Not Disturb” sign to hang outside.

“I enjoyed it and he was a very good lover,” Ms. Davison, 85, said. “That was part of how close we were: physically touching and kissing.”

Ms. Davison is among a number of older Americans who are having intimate relationships well into their 70s and 80s, helped in some cases by Viagra and more tolerant societal attitudes toward sex outside marriage. These aging lovers have challenged traditional notions of growing old and, in some cases, raised logistical and legal issues for their families, caretakers and the institutions they call home.

Nursing homes in New York and across the country have increasingly broached the issue as part of a broader shift from institutional to individualized care, according to nursing home operators and their industry groups. Many have already loosened daily regimens to give residents more choice over, say, what time to bathe or what to eat for dinner. The next step for some is to allow residents the option of having sex, and to provide support for those who do.

“Sex falls right smack dab in the middle of who we are as people,” said Marguerite McLaughlin, senior director of quality improvement for the American Health Care Association, the nation’s largest trade association for nursing homes, representing nearly 10,000 of them.

The Hebrew Home has stepped up efforts to help residents looking for relationships. Staff members have organized a happy hour and a senior prom, and started a dating service, called G-Date, for Grandparent Date. Currently, about 40 of the 870 residents are involved in a relationship.

A resident wore a corsage at the prom. About 40 of the 870 residents at the Hebrew Home are involved in a relationship.

James Estrin / The New York Times

Many others are ready for one. Beverly Herzog, 88, a widow, said she missed sharing her bed. Her husband, Bernard, used to lie on the bed with his arm outstretched. Assume the position, he would tell her. She would curl up beside him. “I hate getting into a cold bed,” she said. “I feel no one should be alone.”

But intimacy in nursing homes also raises questions about whether some residents can consent to sex. Henry Rayhons, a former Iowa state legislator, was charged with sexual abuse in 2014 after being accused of having sex with his wife, who had severe Alzheimer’s disease and was in a nursing home. A jury found him not guilty.

The case helped call attention to the lack of clear guidelines for many nursing homes; only a few, like the Hebrew Home, have any formal policy at all.

Dr. Cheryl Phillips, senior vice president for public policy and health services for LeadingAge, an industry group that represents more than 6,000 nonprofit elder-care service providers, including about 2,000 nursing homes, said sex would come up more often as baby boomers moved in. “They’ve been having sex — that’s part of who they are — and just because they’re moving into a nursing home doesn’t mean they’re going to stop having sex,” she said.

Daniel Reingold, the president and chief executive of RiverSpring Health, which operates the Hebrew Home, said growing old was all about loss: vision, hearing, mobility, even friends. Why should intimacy have to go, too? “We don’t lose the pleasure that comes with touch,” he said. “If intimacy leads to a sexual relationship, then let’s deal with it as grown-ups.”

The nursing home came up with a sexual expression policy in 1995 after a nurse walked in on two residents having sex. When the nurse asked Mr. Reingold what to do, he told her, “Tiptoe out and close the door behind you.”

Before adopting the policy, the Hebrew Home surveyed hundreds of nursing homes in New York and elsewhere, only to find that “most of them even denied that their residents were having sexual relationships,” Mr. Reingold recalled. He later spoke about the findings at an industry conference, asking an audience of more than 200 people if sex was going on in their nursing homes. The only ones who raised their hands were three nuns in the front row, he said.

Today, the sexual expression policy is posted on the home’s website and reviewed with staff members. Mr. Reingold said it was intended not only to encourage intimacy among those who want it, but also to protect others from unwanted advances and to set guidelines for the staff. For instance, the policy stipulates that even residents with Alzheimer’s can give consent for a sexual relationship under certain circumstances.

Though the nursing home has never been sued over the policy, Mr. Reingold said, some families have objected to such relationships, especially if one of the residents is still married to someone else who is not at the nursing home.

Relationships also mean more drama for the staff, which tries to keep up with who is together and who is not. The dining room can be a land mine. Sometimes, one member of a couple will get jealous when the other pays attention to someone else. Other couples become too amorous, prompting calls to “keep it in your room.”

Still, Eileen Dunnion, a registered nurse who has three couples on her floor, said she encouraged her patients to take a chance on a relationship, reminding them, “You get old, you don’t get cold.” A few years ago, she served as a lookout for a man who had two girlfriends. He never got caught. “I did my job well,” Ms. Dunnion said. “Nurses wear many hats.”

Kelley Dixon, 74, said sex had become more important to him because it did not happen as regularly as he would like. “It’s not about bang-bang and I’ll see you later,” he said. “It’s about enjoying the company of who you’re having sex with. I’m not keeping track anymore. I don’t have notches on my gun.”

In the past year, a dozen people signed up for G-Date. Half of them were matched by social workers and sent on a first date at an on-site cafe. None found love, though some became friends. “We’re not giving up,” Charlotte Dell, the director of social services, said. “We’re going to get a wedding out of this yet.”

Francine Aboyoun, 67, is waiting to be set up through G-Date. She said she remained hopeful that she would meet someone. While living at another nursing home, she met a man who would come to her room at night. Though they did not have sex, they kissed and lay together in her bed. “Wow, it felt like I was young again,” she said.

Ms. Davison, who is divorced, said the last thing she ever expected was to find the love of her life at a nursing home. She met Leonard Moche in the elevator. He was smart and made her laugh. She moved to his floor to be closer to him.

Ms. Davison said they had been planning to get married when he suddenly became ill; he died this year. She is still grieving.

“I think of him as my second husband,” she said. “It was great and unexpected, and wonderful while it lasted.”