The small fire have occurred in Richmond and Catterick Garrison.
In the latest incident firefighters were called to a camping chair on fire in Station Road, Richmond, at about 5pm on Monday.
The Richmond crew used a bucket of water to extinguish.
Youths were blamed for starting the fire.
A spokesperson for North Yorkshire Fire and Rescue Service said: “In the past few months there’s been a number of small deliberate fires across Richmond & Catterick Garrison.
“One day the small fire may become a big one.
“Ring 101 to report any information? Do you know where your teenage children are? Are they coming home smelling of smoke?”
