Abstract: In an exercise apparatus comprising a fixed support member (3) and a moving part (2) which can perform movements correlated to the exchange of forces between a user and the apparatus, a support device (1) comprises: elastic supporting means (4); means (6) for damping the movements of the moving part (2) and adjusting means (7). The damping means (6) are arranged parallel with the supporting means (4) and comprise a magnetic actuator (8), in which a first, moving component (9) has an electroconductive element (11), and a second, fixed component (10) comprises a permanent magnet (12) and a non-permanent magnet (13) connected to one another to form at least one air gap (14) which houses the electroconductive element (11). Electrical energizing of the electroconductive element (11), whether generated or induced, applies to the first component (9) of the actuator (8) a reactive magnetic force which opposes the translational movement. [FIG.