Witnesses in the town of Afgoye southwest of the capital say the Hizbul Islam militants on Sunday stoned to death the man accused of adultery and shot the man accused of murder. They say the militants summoned the town's residents to watch the executions.
Islamic courts run by radical clerics have ordered executions, floggings and amputations in recent months. In some areas militants have also banned movies, musical telephone ringtones, dancing at weddings and playing or watching soccer.
Somalia has been ravaged by violence since warlords overthrew dictator Mohamed Siad Barre in 1991, then turned on each other.