Although Miami Dolphins running back Ricky Williams has failed another drug test ? his fourth violation of the NFL's anti-drug policy ? the substance involved was not marijuana, sources said Monday. Marijuana triggered positive tests in 2002 and 2003. The third violation was for dropping out of the substance-abuse program by retiring in July 2004. Williams already has begun the appeal process regarding the latest positive test, a source said. The process is expected to take another four to six weeks. People close to Williams and others in the league would not say Monday what caused the latest violation, which could result in at least a one-year suspension. His agent, Leigh Steinberg, said Monday he is confident that his client no longer is using drugs. "Ricky has been in the best behavioral mode of his life," Steinberg said. "He didn't work this hard to get back only to let that happen." Williams returned to the Dolphins last season and was a success after sitting out a four-game league suspension. The appeal process begins with the NFL Players Association, which already has sent the case to the league for review.