The judges in the cases said the evidence was overwhelmingly contrary to the parents' claims — and backed years of science that found no risk.

"It was abundantly clear that petitioners' theories of causation were speculative and unpersuasive," the court concluded in one of a trio of cases ruled on Thursday.

The ruling, which was anxiously awaited by health authorities, was a blow to families who have filed more than 5,000 claims for compensation through the government's Vaccine Injury Compensation Program. The claims are reviewed by special masters serving on the U.S. Court of Claims.

To win, the families' attorneys had to show that it was more likely than not that the autism symptoms in the children were directly related to a combination of the measles-mumps-rubella shots and other shots that at the time carried a mercury-containing preservative called thimerosal.

But the court concluded that "the weight of scientific research and authority" was "simply more persuasive on nearly every point in contention."

The court still has to rule on separate claims from other families who contend that rather than a specific vaccine combination, the lone culprit could be thimserosal, a preservative that is no longer in most routine children's vaccines. But in Thursday's rulings, the court may have sent a signal on those cases, too:

"The petitioners have failed to demonstrate that thimerosal-containing vaccines can contribute to causing immune dysfunction," a judge wrote about one theory that the families proposed to explain how autism might be linked.