Despite the passage of several laws intended to expand coverage step by step, the number of Americans without insurance has risen steadily, by an average of 1 million a year.

The number of uninsured has increased each year since 1987 and now exceeds 41 million, roughly one-seventh of the population.Moreover, this steady rise has occurred despite a remarkable economic boom. The nation has created more than 14 million jobs since 1993, but most of these are in small businesses, which are far less likely to provide health insurance than are large companies.

In Congress, members of both parties keep returning to the problems of the uninsured, but the cost and complexity of the issue pose extraordinary hurdles, and there is little agreement on how to clear them.

Congress created a new program to finance health care for low-income children last year. And in 1996 it passed the Kassebaum-Kennedy law, to make insurance more readily available to millions of people who change jobs or lose them.

These efforts have made a difference; without them, experts say, the number of uninsured would be even higher.

But there have been problems:

- Federal and state officials say insurance companies have found ways to skirt the Kassebaum-Kennedy law by shunning people with medical problems or by charging them very high premiums.

- Sweeping changes in federal welfare policy may inadvertently increase the number of uninsured children, offsetting some of the expected gains in coverage from the new Children's Health Insurance Program.

- Federal officials had assumed that states would quickly adopt the standards established by the Kassebaum-Kennedy law, but that has not happened.

The plight of the uninsured may seem distant to members of the middle class riding the current economic boom. People are less anxious about losing their jobs and their benefits than they were in the recession of the early 1990s.

But William Custer, an economist at Georgia State University, said, "If the economy slows or if health costs rise much faster than prices in general, we'll probably see more rapid growth in the number of Americans without health insurance."