This article was reproduced with the kind permission
of the British Broadcasting Corporation
27 November 2007, 12:59 GMT
Central Scotland Police said two flats within the same block in Glasgow Road, Camelon, were targeted.
When firefighters arrived at the scene on Monday and Tuesday they found burning material placed against different doors in the block.
The incidents resulted in one man being treated for smoke inhalation.
The first incident happened at 1645 GMT on Monday.
At about 0520 GMT on Tuesday another fire was started within the same block but at a different flat.
Firefighters from Central Scotland Fire and Rescue Service had to assist two residents from the three-storey block using ladders.
A spokesman for police said the incident was now being investigated and that they were following a positive line of inquiry.