An internal combustion engine has an electronically controlled variable mechanical transmission for varying the maximum lift of intake and/or exhaust poppet valves. The mechanical transmission includes a regulator mechanism with one or more slotted holes, and an actuation mechanism. The actuation mechanism includes a primary oscillating lever in contact with a cam actuating the lift of the valve, a secondary oscillating lever directly acting on the poppet valve, and a wedge-shaped slider device. The slider device includes a bore fitted with a roller free to rotate and having its ends protruding from it. The slider is interposed between the two oscillating levers and transmits the movement from the primary oscillating lever to the secondary one. The slider actuates the variation of the poppet valve's maximum lift. The regulator mechanism modifies the angular position of the slotted holes and actuates the variation of the transmission from the cam to the poppet valve.