There is not one "homeless" problem -- in Washington or in the nation -- there are several.

These include:

The decimation of the stock of low-income housing as a result of "gentrification," a growing trend that has upwardly mobile young couples taking over inner-city buildings formerly occupied by the poor;

The inability of unemployed or marginally employed people to find housing they can afford;

The dearth of incentives for real estate operators to supply low-income housing;

The inadequate supply and deplorable conditions of public shelters; and

The unhappy results of the well-intentioned policy of "deinstitutionalization" of mental patients. Mayor Marion Barry Jr. has announced important measures to address at least the last two of these aspects of homelessness. He announced Friday that the city will spend $250,000 to correct some of the awful conditions at the shelter run by the Community for Creative Non-Violence, and he also announced a new policy, based on the New York City model, of physically removing "street people" to shelters and hospitals during freezing weather.

Both are eminently sensible and compassionate moves.

President Reagan, responding to the near-fatal hunger strike of CCNV's insufferable saint, Mitch Snyder, pledged to turn the organization's run-down dormitory into a model shelter. But that pledge, made on the eve of the November 1984 presidential election, was subsequently abandoned when federal authorities failed to reach an agreement with Snyder on how much to spend on the project.

They recently announced their determination to close the shelter and forcibly evict its 600 residents. Fortunately, that threat never materialized, and Barry now has undertaken to meet at least a portion of the administration's abandoned commitment.

That -- philosophically, at least -- was the easy part. Far more difficult is the question of what to do with homeless people who, for whatever reasons, do not wish to use existing shelters. These, it is believed, are mostly confused and frightened former mental patients, released from St. Elizabeths on the assumption that they posed no public threat and would seek counsel and medication at community-based mental health facilities.

If they are sufficiently sane that they no longer need be kept in hospitals against their will, how can they be crazy enough to be forced into shelters? The American Civil Liberties Union, arguing the right of these pitiful people to make their own decisions, even if the cost is their lives, is challenging the policy of New York's Mayor Ed Koch that authorizes the police to transport forcibly "street people" to public shelters when the temperature falls below 32 degrees.

You don't have to be a Big Brother authoritarian to understand that, in this case, the ACLU is wrong and Koch is right. So is Barry, whose new policy will provide transportation for those who choose to be taken to shelters and dispatch city crisis workers to interview those who don't. Those deemed mentally incompetent will be taken to D.C. General Hospital for further evaluation. What it amounts to is a bureaucratically clever way of keeping crazy people from freezing to death.

But Barry's new policy, laudatory as it is, does not address the other causes of homelessness: the shortage of low-income housing and persistent unemployment.

For those who, though clinically sane, become "street people" because they have no money, no job and no prospects, the problem is a good deal tougher, and far more expensive, to solve.

It may, given the city's sluggish economy, be essentially unsolvable. For though it looks like a housing problem, when you see these hapless people sleeping on park benches and steam grates, the fact is there problem is economic. They need jobs, and the jobs aren't there.