The first incident happened at 6pm on Sunday on London Street, near the corner with Drummond Place, when a 25-year-old victim was grabbed by a man who had tried to pull her bag from her shoulder.
She was shoved to the ground by the suspect, who fled empty-handed with two other men. He is described as white, 17 to 18 years old, medium build, with short brown hair wearing a light blue T-shirt.
In the second incident at around 7pm, a 20-year-old woman was with her mother on Leith Street when they were approached by two suspects, who took her handbag. The first suspect is described as white, 24 to 25-years-old, with short light blond hair wearing baggy navy blue bottoms, and a dark zipped top. The second is described as white, of medium build wearing dark Adidas bottoms.