TRIPOLI, Libya—Triumphant rebel fighters and thousands of ordinary Libyans stormed Col. Moammar Gadhafi's fortress compound here Tuesday after a daylong battle, but the elusive strongman was nowhere to be found.

Antiregime troops waged fierce battles at the gates of Bab al-Aziziya, Col. Gadhafi's longtime home and headquarters. When rebels breached one of its gates in the late afternoon, Tripoli residents joined in to cheer and embrace.

With...