In a further blow to the antivaccine movement, three judges ruled Friday in three separate cases that thimerosal, a preservative containing mercury, does not cause autism.

The three rulings are the second step in the Omnibus Autism Proceeding begun in 2002 in the United States Court of Federal Claims. The proceeding combines the cases of 5,000 families with autistic children seeking compensation from the federal vaccine injury fund, which comes from a 75-cent tax on every dose of vaccine.

Families of children hurt by vaccines — for example, who suffer fatal allergic reactions — are paid from it but are unable to sue the vaccine manufacturer. The fund has never accepted that vaccines cause autism; the omnibus proceeding, with nine test cases based on three different theories, was begun in 2002.

The antivaccine groups also lost the first three cases, which were decided in February 2009 by the same three judges, known as special masters. All three rulings were upheld on their first appeals.