The numbers are staggering. Tens of thousands of workers who say they are victims of asbestos-related diseases. Millions of dollars in court costs, lawyers' fees and medical expenses. Dozens of companies once prosperous from making asbestos struggling to stay afloat.

Behind the numbers are people like Edmund F. Cooper, 68, who worked in the boiler rooms of large hotels and office buildings in the Washington area for years and has mesothelioma; Andrew R. Youngbar, 42, who has worked at the Bethlehem Steel Sparrow's Point plant near Baltimore since he was 18, who has asbestosis; Priscilla Killeen, 47, whose husband, James, was a sheet-metal worker who died last year of lung cancer at the age of 52.

The victims of these diseases say the companies that made asbestos knew it was harmful long before the workers did -- and should now bear financial responsibility for the harm to their health.

The companies, by and large, reply that they did not know of the risks involved, and they question in many cases whether health problems were caused solely -- or even principally -- by exposure to asbestos.

Cooper, like many workers who say they were exposed to asbestos, has worked in a number of locations where the insulating material was used. For him, the exposure began in the boiler rooms of Navy ships in World War II and moved to the office buildings and hotels in Washington and suburban Maryland where he was a stationary engineer -- someone who maintains boilers and cooling systems.

"I was never aware of the dangers," Cooper said recently.

Though he had worked with asbestos for decades, Cooper's first indication that it was dangerous came about 1985, he said. The District's Executive House Hotel at 15th Street and Rhode Island Avenue NW, where Cooper worked, was being remodeled. When the ceilings were pulled out, District inspectors pointed out that the duct work was covered with asbestos and it would have to be removed.

Teams of men came in and draped the area with plastic. Big yellow signs were posted: Danger. Do Not Enter Area.

"I heard the electricians talking. People were saying, 'They've got asbestos. I'm staying clear,' " Cooper recalled. "At that point, I'd been around asbestos for 40 years."

Plaintiffs' attorneys estimate that in the Washington area there are 8,000 to 9,000 asbestos-related plaintiffs, most of them in Maryland, where they worked for the construction and building trades or in the steel mills of Baltimore. Many of them are among the more than 100,000 workers with claims against the fund set up by Manville Corp., once the country's largest maker of asbestos.

But Manville is only one of many companies that at one time produced the flaky white material used to insulate pipes, boilers, coke ovens and cooling equipment. Several dozen companies made asbestos, and they or their successor firms are named as defendants in courts across the country by workers who contracted lung cancer and other diseases years after making or using asbestos products. The workers' lawsuits, typically filed against multiple companies, charge that the companies knew about and concealed the dangers of asbestos. Some of the companies have set up trust funds to pay off claims, others have filed for bankruptcy while still others are litigating the cases one at a time, paying off claims out of profits.

Widespread use of asbestos was curtailed in the early 1970s after the government became aware of the health risks it posed. But because it had been used in the construction of buildings, workers continued to be exposed to it.

The legal situation has left U.S. courts jammed with cases involving asbestos. And the awards or settlements vary wildly -- from no award at all to millions in some cases -- depending on how sympathetic the plaintiff appears and the luck of the draw with the jury, among other factors.

Just last week, a jury in a federal court in the Virgin Islands awarded $26.3 million to a man with asbestosis, a progressive hardening of the lungs. It was one of the largest awards ever in an asbestos case. Owens-Corning Fiberglas Corp., which has settled close to 50,000 cases, plans to appeal the judgment. Legal experts said the jury's award, which appeared excessive relative to settlements and awards in similar cases, reflects the need for a standard settlement mechanism outside the courts.

Companies that once made asbestos contend that while there are many claims, only a small percentage of them actually have merit and that there are many other products and lifestyle factors that cause diseases such as lung cancer.

When workers find they have asbestos-related diseases, they must try to remember and identify the labels that companies used on asbestos packaging as far back as World War II to determine which companies they should sue. Then, they must find witnesses who can testify that they were exposed to the material. The process can take years. Many of the plaintiffs have died waiting for their awards.

In February 1987, Cooper discovered he had mesothelioma, a fatal disease of the lungs that is caused only by asbestos. He had surgery to remove a tumor. Though he has filed a legal claim, Cooper is upset that his case is not set for trial until 1992.

"The family knows this particular disease is fatal," said Cooper. "The kids are pretty young, but we've talked to them about it. They ought to know what's going on."

The victims, along with widows and children of asbestos victims, have gone to support groups. Some, like steel plant worker Youngbar, have already been compensated by some companies. But, they ask, what good is the money when you sit around at night wondering what will happen to your family when you're gone?

Some Washington-area asbestos plaintiffs have carefully monitored the recent settlement proposed for the Manville trust cases. The $3 billion Manville Personal Injury Settlement Trust was set up in 1987 following Manville Corp.'s filing for bankruptcy several years earlier because of the flood of lawsuits filed against it.

The trust said earlier this year that it was virtually broke after paying about 20,000 claims. Federal judges have criticized the trust and plaintiffs' lawyers for high legal fees that have dissipated the fund. But under a settlement proposed to resolve a number of suits against the trust, Manville Corp. would pay the trust up to an additional $520 million over the next seven years.

According to the proposal, an average payment of $146,000 would be paid to victims of mesothelioma; $120,000 for nonsmokers who are victims of lung cancer; $70,000 to lung cancer victims who also smoked; $20,000 to victims of other cancers; and $80,000 to victims of nonmalignant diseases. In the less serious illness category, an average of $35,000 would go to asbestosis sufferers and $12,000 to those with pleural disease, which affects the lining of the lungs. Those amounts would be paid out in increments over several years, with the most seriously ill being paid first.

Workers like Cooper and Youngbar who have claims pending against the trust still are not satisfied with the plan.

"People I work with who are in their 60s are suffering and need the money now," said Youngbar. "They'll be dead {by the time they get their settlements}. That's wrong."

Youngbar, though he is only 42, sounds like an older man because of his shortness of breath caused by a form of asbestosis. He has worked at Sparrow's Point for 25 years, having started as a mechanical helper when he was a teenager. Now he's a general foreman with nearly 150 workers reporting to him.

In 1980, when he was just over 30, he found that when he played softball, he couldn't run without getting short of breath. "It scared the hell out of me," said Youngbar. "I was 31 years old, driving home thinking about my wife and my kids. How do you come home and tell your wife?"

When workers and their representatives point fingers, it is not only the manufacturers they look to. Others were also silent about the hazards, they say.

"These people were working for the U.S. Navy during World War II," said one source close to the cases. In addition, the government controlled supplies of asbestos during the war. " ... To say 40 years later that 'it's not our problem' is absurd."

Thus far, the government has been successful in opposing all legal efforts to include it as a defendant in the suits. And legislative campaigns to mandate a fund set up by the government like the one established for coal miners who suffered from black lung disease have failed.

While the victims and families are frustrated with the legal process, they are even more outraged that they were not given information by someone sooner.

Priscilla Killeen said she is resentful and bitter. Her husband, James E. Killeen Jr., was a healthy, vigorous 51-year-old when he was told he was going to die. Five months later, June 1, 1989, he died of lung cancer.

James Killeen belonged to a group -- sheet-metal workers -- that has one of the highest levels of exposure to asbestos outside of those who manufactured the product. They often worked in confined spaces with the product whose fibers could stay in the air for days at a time.

"When you love someone and lose them, you want to say to the company: 'Why didn't you tell us?' You want to know if there's something you could have done," said Priscilla Killeen, 47, who works for the Sheet Metal Workers Local 100. "He was very angry," she said of her husband. "How can you justify working for somebody who knew and didn't tell you?"