Detectives are trying to establish whether the same man is responsible for both incidents, which happened within five days in Peebles.
On Saturday, a 41-year-old woman was walking along a footpath by Dovecot Road when a man grabbed her and tried to pull her backwards.
The victim screamed and struck out at her attacker before fleeing to a relative's home and contacting police.
Her attacker is described as white, late 30s, 5ft 10in tall with a gaunt, unkempt appearance, and a scar below his right eye.
Last Tuesday, a 52-year-old woman was working in a store when a man tried to push her against a wall. He was fought off and fled the premises.