After resolving the latest round of legal hurdles, a Los Angeles judge has scheduled a hearing for next week to decide whether Lyle and Erik Menendez should be eligible for release after more than three decades behind bars.

The long-awaited resentencing hearing, which had first been scheduled for December and then was repeatedly postponed will now take place over two days, on May 13 and 14, the judge, Michael V. Jesic of Los Angeles Superior Court, said on Friday.

Once again, family members of the brothers were arranging to travel to Los Angeles for the proceedings. Others, including people who were imprisoned with them and correctional officials who have overseen their incarceration, were planning to be there, too, to testify that the brothers have been rehabilitated and no longer represent a danger to the community.

The Menendez brothers have been behind bars since the spring of 1990, when they were arrested and charged with killing their parents the previous summer. The brothers had burst in to the den of the family home in Beverly Hills, Calif., and killed their parents with shotgun blasts as the couple watched television and ate ice cream.

The crime, and the fact that it occurred in such a wealthy, exclusive community, captivated the country. And the case never fully ceded its grip on the nation’s consciousness, maintained through numerous dramatic and documentary treatments.

At their trials, the brothers had maintained that they had been sexually abused for years by their father, Jose Menendez, and that their mother, Kitty Menendez, was complicit because she knew of the abuse and did nothing to stop it. They said they killed out of fear for their own lives, worried that their parents would kill them first to prevent disclosure of the family’s secrets.