The first involved a derelict barn in Scalby, where rubbish and straw had been set alight.
Crews were called to Station Road at around 8.45pm and used a main jet to put out the fire.
A garage fire was also reported at Albemarle Crescent in Scarborough shortly before 5am.
A North Yorkshire Fire Service spokesman said: "This was a wheelie bin fire, believed to have been due to a deliberate ignition."
He said a hose reel was used to put out the flames.