A double-cylinder circular knitting machine for hosiery or other knitted articles comprises a lower needle cylinder with a vertical axis and an upper needle cylinder arranged above and coaxially to the lower needle cylinder. Aligned axial slots are formed on the lateral surface of the lower and upper needle cylinders. Each of the axial slots of the lower and upper needle cylinders accommodates an actuation element which can engage a needle to be actuated and is provided with a fixed heel, and with a heel which can be extracted radially on command from the axial slot. The transfer of a needle from one needle cylinder to the other is performed by fixed cams and by a selection device producing transition into the extracted position of the movable heel exclusively of the actuation elements that correspond to the needles to be moved to the lower needle cylinder.