A variable valve train for actuating a plurality of gas exchange valves of an internal combustion engine includes a plurality of individual cam sleeves axially displaceable relative to one another and disposed so as to form the camshaft. Each of the plurality of individual cam sleeves include a plurality of different cam profiles. A switching shaft is disposed inside the plurality of cam sleeves and is configured to rotate together with the plurality of cam sleeves. A switching ball operatively connects one of the plurality of cam sleeves to a switching contour disposed on the switching shaft. A displacement piece is disposed so as to be rotationally engaged but axially displaceable on one of the plurality of cam sleeves and connected to the switching shaft. An actuator is operatively connectable to the displacement piece by the switching ball so as to displace the one of the plurality of cam sleeves.