Both were threatened with knives in the separate incidents last Monday evening in Drumoghill and Knockbrack areas.
The first victim, the woman, had personal possessions and a handbag taken. The empty bag was later found dumped in Lismonaghan.
The elderly man had a knife waved at him.
Gardaí say that although neither victim was physically injured, they were left absolutely traumatised by the attacks.
The raids come after a break-in at Royal and Prior school in which classrooms were ransacked.
Gardaí are appealing for anyone with information on any of the incidents to contact Letterkenny Garda Station on 074 91 67100.