The first incident took place at RS McColl in Parbroath Road around 8.20pm, with the second taking place at RS McColl in North Street around 8.45pm.
Two men have entered the premises and threatened a staff member with a knife before demanding money and goods. In both incidents, they have left empty handed.
The first suspect is described as in his early twenties, 5ft 8ins tall, of stocky build, with his face obscured, wearing a black and white striped top, dark-coloured trousers and dark-coloured trainers.
The second suspect is described as also being in his early twenties, 5ft 8ins tall, of medium build, with his face obscured and wearing a dark grey hooded tracksuit top and light-coloured tracksuit bottoms with two dark-coloured pockets on the rear.
Detective Inspector Chris Mill of CID in Fife Division said: “Both of the staff members have shown great courage during what was a distressing experience and we are pursuing a number of lines of enquiry to trace the perpetrators.
“Given the distance between the two premises, it’s possible that a vehicle or bikes were used and we’re urging anyone in the local community who may have seen these men, or any suspicious vehicles in the area, to get in touch as soon as possible.
“We’d also ask any local business owners or staff members who may have seen the men described within their shop earlier in the day to contact us.
“Be assured that we will use all resources at our disposal during this investigation, but please remain vigilant and report any suspicious behaviour to us on 101, always dialling 999 when a crime is in progress.”
Anyone with information can contact Police Scotland on 101, quoting incident number 2924 of 2nd January, or report this anonymously to the charity Crimestoppers on 0800 555 111.