An unclean air filter or dirty gas burners could develop this issue. Alternately, the burners might require changing or something could be obstructing air flow to the combustion chamber.
If the air filter is unclean, then you must replace it as quickly as possible. If the burners are unclean, then you must clean them. If the burners require to be changed, you will have to call an expert technician. Likewise, make sure that absolutely nothing is blocking airflow to the combustion chamber.
If your system keeps turning on and off regularly, you may have a thermostat problem. Other possible causes could be a dirty air filter or an issue with the blower motor.
Initially, change your dirty air filter. If you have a mechanical thermostat, try adjusting the heat anticipator. If you have an electronic thermostat, follow the directions consisted of with the gadget to troubleshoot any possible issues. If this still does not address your problem, you might have a blower motor problem. Try oiling the blower motor lubrication ports which are generally found at each end of the shaft. Inspect the tension in the motor belt. If it is too loose, tighten it. If it is frayed, replace it.
If your system's fan is running non-stop, you might have the system set to "constant." If your thermostat does not have a "fan" setting but it still runs without stopping, you could have a problem with your fan limitation control switch.