There is described a support system enabling supporting an object such as a platform (1) free from vibration, in that bearing elements (50) have a stiffness (k) which at a working point (z0) equals zero. A bearing element (50) comprises two magnetic couplings (51, 52) provided by permanent magnets (61, 63). One coupling (51) has a positive stiffness (k51), and the other coupling has a negative stiffness (k52); in the working point, the absolute values of those stiffnesses are equally great. Alternatively, electrostatic couplings are used.