A heat-and-electricity supply system in which steam from a steam generator is utilized to supply an electric output and a heat output such a system includes: a steam turbine driven by the steam generated in the steam generator; a clutch with reduction gear, connected to a shaft of the steam turbine; a power generator for providing the electric output, connected to the clutch with a reduction gear; a clutch with a speed increasing gear, connected to a shaft of the power generator as occasion demands; a compressor connected to the clutch with speed increasing gear; a heat-side load utilizing a cooling medium or a heating medium supplied from the compressor.