A combined heat and power system comprising a Stirling engine (1) the head (2) of which is heated by a burner. A heat exchanger (10) absorbs heat from exhaust gases from the burner which have heated the engine head. A supplementary burner (22, 23) generates additional heat which is directly absorbed by the heat exchanger. The supplementary burner is a multi-stage burner with separate stages (22, 23) which are independently controlled.