In one of the crimes, the victim was walking to her car in a shopping center parking lot when a car approached her.
A woman reached out from the car's passenger seat and grabbed the victim's shoulder bag. Police say the victim was dragged by the car until her purse broke free and the thieves fled.
Nassau County police say similar robberies were reported at several locations on Long Island over the past week.
Police on Sunday said they had arrested 30-year-old Veronica Sarabella and 29-year-old Alfonso Zitoli. They were arrested on charges of robbery, attempted robbery and grand larceny. No information on an attorney for the pair was available.