The gang members – who spoke with foreign accents – threatened female staff in both incidents, said Supt Kevin English.
In the first incident, an assistant at a chippie in Muff had her hands tied behind her back and masking tape placed over her eyes and mouth as the gang threatened her with a knife.
This raid, at around 9.30pm on Monday past, involved threats of violence against the terrified woman working at Annie’s Diner.
The gang made off with the day’s takings.
The woman was able to free herself and raise the alarm a short time later.
The raiders – believed to the same gang – struck again in broad daylight in Buncrana around 3.40pm yesterday afternoon.
The three men walked into a fashion store on Main Street where they also threatened a female member of staff.
They tied her up using the same plastic ties used on Monday – and also covered her mouth and eyes with masking tape.
Supt English said threats of violence were used before the gang left with a sum of money.
“I don’t like labelling people but we believe those involved were foreign nationals,” he said.
The leading Garda said it was also his belief that both raids were planned in advance and the gang members may have been in both areas for days beforehand.
“This is an extremely rare sort of crime for this area,” said Supt English who appealed for anyone with information to contact Buncrana Gardai.