A linear compressor has a rigid frame (11, 12, 13), on which an oscillating body (16) is held via at least one spring (9) so as to be able to effect reciprocating motion and at least one electromagnet (14, 15) is mounted for driving the reciprocating motion of the oscillating body (16), and having a pump chamber (13) forming part of the frame, in which pump chamber a piston, connected to the oscillating body (16), may effect reciprocating motion. The frame (11, 12, 13) is connected in an oscillatory manner to a fixing member (1) for fixing the linear compressor to a support by a diaphragm spring (5, 7, 9) oriented transversely of the direction of movement of the oscillating body.