Sitting among the other people using the computers at the Vineyard Haven library on a bleak, icy day this week, Jon and Rick blend right in. The only hints of their difference are a couple of small piles of possessions nearby.

These men are homeless, and for them, the primary purpose of coming here is not research or reading, but warmth.

It would no doubt come as a surprise to the other Vineyarders tapping away at adjacent terminals to know this. It might even surprise them that homelessness exists on the Island.

But the real surprise comes when you begin to talk to them, for they defy stereotypes about homeless men. They are not mentally ill, they are not substance abusers — although both smoke occasionally and Jon harks back fondly to the days when he could sip a single malt scotch. They are not smelly or aggressive; they are, as their new guardian angel Connie Teixeira says, “quite and gentle souls.”

And Jon in particular is very articulate.

He is the first to concede he is the less unlucky of the two. He is of retirement age, and after working for 20 odd years for the state, he receives a pension of about $15,000 a year. But that’s his entire income; because he is on a pension he receives no Social Security.

Because of his age, he also can go to the Tisbury senior center to eat lunch each weekday. So even if he can’t afford to have a roof over his head, he’s not going to starve.

Just as well, he said wryly, for it means he won’t be forced into a life of crime in order to get by.

“At my age,” he said, “the fast getaway is no longer an option.”

He walks with a cane. It was August 11 when he became homeless, after the money he had gotten for the sale of a quarter share in his mother’s house ran out.

What did he do then?

He began sleeping, he said, behind “pretty much any door that isn’t locked.”

He came into contact with the police a couple of times, but he’s never been arrested.

“One time the police came, I had to ask them to help me up,” he said. “They were pretty good. One of them said ‘Well, John I wish there was some way I could help you, but I don’t know anywhere you could go.’

“I said ‘I know, I’m not blaming you. Thank you for the courtesy.’ ”

And that is what makes homelessness on Martha’s Vineyard a greater hardship than

homelessness elsewhere in the country. There is literally nowhere for such people to go. There are no shelters here, not even, says Connie Teixeira, the woman who has lately become Jon and Rick’s guardian angel, a subway grate to sleep over.

Jon has put his name down for senior housing, but the waiting lists are long. He does not hide his frustration that other people are being accommodated, even though they have houses to sell, while he must wait, homeless.

But his encounters with other homeless people — he’s met four or five others, he said — make him feel comparatively lucky.

“I just want a place to sleep. That’s all. A lot of people don’t have anything at all. So they’ll do something. They’ll go to — just using this as an example — Reliable supermarket, say, or the Stop and Shop, take something, and wave it, and walk out the door. Just because they need a place to sleep and they’ll do just about anything to get it.”

Rick, the less lucky of the pair, concedes he has thought about committing a crime to get warmth and food in jail.

“It’s crossed my mind, but I’d rather have my freedom,” he said.

His homelessness began in mid-September. He had come to the Island to live with a woman, but she kicked him out. Then he lost his job.

“I have no income whatsoever at the moment. No savings left. Everything I had I’ve spent already,” he said.

“I never thought it would happen to me,” he said. “Not in my wildest dreams.”

He had always worked, “at everything from a lumber yard to restaurants.” Over the past four months, he has applied for numerous jobs, he said.

“But with the economy the way it is now, there’s just nothing,” he said.

When it first happened, he said, he was “totally lost.”

“That first night, I found an abandoned house that was open. I’ve slept outside, too. Later, a friend of mine pointed me in the direction of an abandoned trailer, which I was sleeping in before Connie found me. I think it was colder inside than out.

“You adapt, though, you know?”

They have learned the ropes of homelessness, these two. Rick can’t go to the senior center for food, but he goes to the Island Food pantry. Two churches, the Old Whaling Church in Edgartown and Grace Episcopal Church in Vineyard Haven host free suppers on Monday and Friday nights. Grace Church also now leaves bags containing food, soap, toothpaste and water, on the coat rack just inside the door. The library provides warmth and computer access and the ferry terminal provides warmth and television.

The big lucky break for the two men came a bit before Christmas, when Jon fell into conversation with Connie at the senior center.

Like most, she was not aware of a homelessness problem here. But after talking to Jon, she said, “I was in bed one night, and a still, quiet voice said: ‘You can help.’ ”

She began by going to the Tisbury selectmen, and suggesting maybe the school could be used to house homeless people over Christmas. That didn’t happen — there were concerns about insurance liability among other things — but she kept on meeting people and advocating.

The list of those to whom she has spoken now is long, including the all-Island selectmen, state Sen. Robert O’Leary and Rep. Tim Madden, Vineyard housing authorities, elderly housing, Habitat for Humanity, the police and sheriff’s department the county administrator, Island churches, mental health centers, councils on aging, health council, the list goes on.

But her big breakthrough came when a couple of local inn owners, who do not want to be identified, offered rooms: one for 10 days and the other for a week, to Jon and Rick.

That accommodation runs out today. One of the banks, Ms. Teixeira said, had offered a house, but there was no land to put it on.

“You can’t put it in any residential neighborhood because nobody would want it. Not all homeless people are gentlemen like these two. Then, even if you got it, there’s the problem of what umbrella you go under because of the liability concerns for insurance.

“There are so many layers of things you have to get through to get there.

“I have asked a hotel, who have an ad in the paper, if they would discount their rate for a month so that we could maybe get funds together and at least find a place to put these people for a month.”

Tisbury selectman Tristan Israel now is planning a benefit concert for the homeless, on Feb. 13 at the Katharine Cornell Theatre.

“I hope people will come so we can raise a little money, even if it’s only enough to put them in a hotel for a day or two,” he said yesterday.

“At least I think we’ve reached some awareness now on the Island that we have a problem. And with the governor’s cuts to programs that serve the homeless across the state, the cuts in mental health services, we are going to have more of them.”

Ms. Teixeira agrees.

“At some point next month, I’m told, we will have at least two families who are going to be foreclosed on,” she said.

Ms. Teixeira hails originally from Washington, D.C. a place with far bigger poverty problems than the Vineyard. And yet, she said, in some ways the plight of the homeless is worse here, with no infrastructure to deal with it.

“What we badly need is somewhere for emergencies, when people need a place to go, tonight. And then we need a transitional place, while we work out where else they need to be. Then you need elderly housing or affordable housing, for when people are getting back on their feet and just need somewhere affordable to stay,” she said.

Getting all that looks like a monumental task, and she readily admits this is the hardest thing her little interior voice has ever asked her to do.

But she’s plugging away at it, refusing to accept that on the Vineyard, a place where most of the houses are people-less for most of the year, there is no house for the homeless people.