A double-cylinder circular knitting machine for hosiery or other knitted articles, comprising a lower needle cylinder which has a vertical axis and an upper needle cylinder which is arranged above and coaxially with respect to said lower needle cylinder; mutually aligned axial slots being formed on the lateral surface of the lower needle cylinder and on the lateral surface of the upper needle cylinder, each of the axial slots of the lower needle cylinder and of the upper needle cylinder accommodating at least one element (10,10') for actuating a needle; said actuation element (10,10') being engageable, by means of one of its ends. with the head (6a,6a') of a needle and being provided with at least one fixed heel (3 a), which protrudes radially from the lateral surface of the corresponding needle cylinder (1,1') to engage actuation cams (8,8'; 9,9') which are arranged around the lateral surface of the needle cylinders (1,1') and form paths which can be followed by said fixed heel as a consequence of the actuation of said needle cylinders (1,1') with a rotary motion about their own axis with respect to said actuation cams (8,8'; 9,9'), at least the actuation elements arranged in the lower needle cylinder are provided with a heel which can move on command from an active position, in which the heel protrudes radially from the corresponding axial slot of the needle cylinder to engage said actuation cams, to an inactive position, in which the heel is contained in said axial slot of the needle cylinder so as to not engage said actuation cams, and vice versa, characterized in that, for transferring the needles from one needle cylinder to the other, it comprises, sequentially along the path followed by the actuation elements as a consequence of the rotation of the needle cylinders with respect to the actuation cams: - an upper fixed lowering cam, which can be engaged by the actuation elements arranged in the upper needle cylinder for their lowering into a position for engaging the upper head of the corresponding needle, and a lower fixed lifting cam, which can be engaged by the actuation elements arranged in the lower needle cylinder to raise them into a position for engaging the lower head of the corresponding needle; - a transfer selection device, which is adapted to move the actuation elements that correspond to the needles to be transferred into the lower needle cylinder so that their movable heel is in the active position, and an upper opening presser, which can engage the actuation elements arranged in the upper needle cylinder to produce their disengagement from the upper head of the corresponding needle; - a lower fixed lowering cam, which can be engaged exclusively by the actuation elements arranged in the lower needle cylinder and moved with their movable heel into the active position by said transfer selection device; - a lower opening presser, which can be engaged exclusively by the actuation elements that are arranged in the lower needle cylinder and are arranged so that their movable heel is in the inactive position in order to disengage them from the lower head of the corresponding needle; - an upper closure presser, which can engage the actuation elements arranged in the upper needle cylinder for their engagement with the corresponding needle, if present; - an upper fixed lifting cam, which can be engaged by the actuation elements located in the upper needle cylinder. - an upper fixed lowering cam, which can be engaged by the actuation elements arranged in the upper needle cylinder for their lowering into a position for engaging the upper head of the corresponding needle, and a lower fixed lifting cam, which can be engaged by the actuation elements arranged in the lower needle cylinder to raise them into a position for engaging the lower head of the corresponding needle; - a transfer selection device, which is adapted to move the actuation elements that correspond to the needles to be transferred into the lower needle cylinder so that their movable heel is in the active position, and an upper opening presser, which can engage the actuation elements arranged in the upper needle cylinder to produce their disengagement from the upper head of the corresponding needle; - a lower fixed lowering cam, which can be engaged exclusively by the actuation elements arranged in the lower needle cylinder and moved with their movable heel into the active position by said transfer selection device; - a lower opening presser, which can be engaged exclusively by the actuation elements that are arranged in the lower needle cylinder and are arranged so that their movable heel is in the inactive position in order to disengage them from the lower head of the corresponding needle; - an upper closure presser, which can engage the actuation elements arranged in the upper needle cylinder for their engagement with the corresponding needle, if present; - an upper fixed lifting cam, which can be engaged by the actuation elements located in the upper needle cylinder.