The crimes happened at all corners of Fresno starting late Thursday on West Shaw. One of the purse snatchings happened in Clovis.
Officers caught the suspects Sunday night in Downtown Fresno.
Police say so far six women have reported being robbed of their purses during the three-day spree. Many of the victims were injured when they were pulled to the ground by their purse straps.
The suspects now in custody are 33-year-old Robert Deminson, his 18-year-old brother Bebless Demison, and 25-year-old William Garcia.
Authorities have not released their pictures because of the ongoing investigation.