A circular knitting machine for hosiery or the like, which comprises at least one needle cylinder which has a vertical axis and on the lateral surface of which there are axial slots. Each of these axial slots accommodates a needle (106) and an actuation element (110) for the needle (106) which can engage, with one of its ends, the needle (106) arranged in the same axial slot. The needle (106) or the actuation element (110) is provided with a fixed heel (103a), which protrudes radially from the axial slot, and a movable heel (104a) which can be extracted radially on command from the axial slot. Actuation cams are arranged around the needle cylinder and can be engaged by the fixed heels (103a) and by the movable heels (104a) in the extracted position. The machine can perform the usual knitting of known types of machine despite having an actuation cam set which has an extremely small number of actuation cams which can move for activation or deactivation, or none at all.