The first incident took place in the wooded grounds of Northern General hospital at around 8.10pm last night, when arsonists set fire to some rubbish.
They were then called out to a wheely-bin fire in Dryden Way, Southey Green at 10.20pm.
At 1am, firefighters were called out to Palmer Street in Hyde Park, Doncaster to extinguish rubbish fires believed to have been started deliberately.