The invention relates to an external combustion engine, in particular to a rotary external-combustion engine and a rotary external-combustion generator. The invention is characterized in that a working medium is heated to convectively circulate and generate power to drive rotation, and the circulation can be closed circulation. The rotary external-combustion generator utilizes heat absorbed by a heat pump as a heater to lead the working medium to be heated to convectively circulate and generate power to drive rotation and generate power. The thermodynamic cycle is mainly finished by heating and working of the heater, so that the heat loss in cooling and heat releasing can be reduced or avoided. In the invention, the structure is simple, the pollution is less, the efficiency can be obviously improved, the use of circulatory cooling water in a heat power plant can be greatly reduced, and the earth can be properly cooled if the surface water, the underground water, the rivers, the lakes, the seas, the air and the like are used as external heat sources.