The system for driving a reciprocating compressor comprises a reciprocating compressor (1) with a crankshaft (31). A Stirling engine (50) is drivingly connected to the crankshaft (31) of the reciprocating compressor (1). A heat source (71), for example a waste heat source, provides heat to the hot end of the Stirling engine. Heat is partly converted into mechanical power to drive the reciprocating compressor (1).