In the first case, a blue-coloured Ford Focus car parked in Drummond Road was entered and a handbag stolen.
The bag contained a small amount of cash, debit and credit cards, personal items and perfume.
In a second theft, a black Peugeot 207 car which was parked in Princes Avenue overnight was entered and a Tom Tom sat nav and a phone charger stolen.
PC Jim Tweedie at Annan said: “Clearly someone has been prowling about the streets overnight Wednesday and Thursday looking for the opportunity to steal from cars.
“We are appealing for anyone who may have seen or heard anything suspicious to get in touch if they can help identify those responsible.
“Likewise, it may be the case that other vehicles may have been entered although nothing stolen.
“Again, we want to hear from anyone who thinks that their vehicle may have been entered.”
Police are keen to enforce the message that all vehicles left unattended should be secured.
PC Tweedie said: “I would take this opportunity to remind drivers to ensure that vehicles are locked and secure, no matter how short a a time they may be away from them, and of course to make sure that nothing is left on view which might give a thief the temptation to break into the vehicle.
“Property should be removed, or at least placed out of sight when left in the vehicle.”