In a blow to the movement arguing that vaccines lead to autism, a special court ruled on Thursday against three families seeking compensation from the federal vaccine-injury fund.

Both sides in the debate have been awaiting decisions in these test cases since hearings began in 2007; more than 5,000 similar claims have been filed.

In the three cases, each decided by a judge called a special master, the court found that the families had not shown that their children’s autism was brought on by substances in the vaccines  either the measles virus in the measles, mumps and rubella vaccine, or its combination with thimerosal, a mercury-based preservative that was used in most childhood vaccines until 2001.

In a case pitting the family of Michelle Cedillo, a severely autistic child, against the Department of Health and Human Services, the judge ruled that the Cedillos had “failed to demonstrate that thimerosal-containing vaccines can contribute to causing immune dysfunction, or that the M.M.R. vaccine can contribute to causing either autism or gastrointestinal dysfunction.”