A gang of five men locked a man in his 60s in his shed at Linsfort, Buncrana on Tuesday at around 7.30pm, after forcing entry into his home.
They demanded cash and assaulted the man, causing minor injuries. The gang fled the scene after locking the man up.
He managed to free himself and raise the alarm. A small amount of cash was stolen.
A short time later, at around 9pm, a gang of five men assaulted an 80-year-old woman at Ture, Muff, close to the border with Co Londonderry.
Cash was demanded from the elderly woman and she received minor injuries in the attack.
Gardaí are still trying to establish if anything was taken.
Investigating officers believe a blue/grey Proton car with a Northern Ireland registration plate may have been used in both incidents.