A linear-acting, free-piston internal combustion engine suitable for operation on a four-stroke engine cycle comprises a power piston (11a, 11b) reciprocating in a power chamber (18a, 18b) and a compression piston (23, 23a, 23b) reciprocating in a compression chamber (29a, 29b). The power piston (11a, 11b) and the compression piston (23, 23a, 23b) are rigidly connected by means of a rod (19). The compression piston (23, 23a, 23b) performs alternately an intake stroke and a compression stroke and the power piston (11a, 11b) performs alternately a power stroke and an exhaust stroke.