TRIPOLI, Libya — For decades, bearded men in Libya were afraid to walk in the streets or go to the mosque, worried that to be seen as an Islamist would land them in prison, or worse.

As Libya’s leader, Moammar Gaddafi regarded Islamists as the greatest threat to his authority, and he ordered thousands of them detained, tortured and, in some cases, killed. The lucky ones fled the country in droves. But with Gaddafi now in hiding, Islamists are vying to have a say in a new Libya, which they say should have a system based on Islamic law.