To allow both the valve lift and valve timing for an engine valve to be varied in a continuous manner, the variable valve actuating device (1) comprises a camshaft (8) rotatably supported by a fixed part of the engine and provided with a cam (7), a first rocker arm (9) pivotally supported by a fixed part of the engine, the first rocker arm being provided with a first point (12) engaging a stem of an engine valve (6), a drum (11) rotatably supported by a fixed part of the engine and at least partly surrounding the cam, a second rocker arm (10) having a first point (20) pivotally supported by the drum, a second point (21) adapted to engage the cam and a surface engaged by a second point (22) of the first rocker arm, and a control member (25, 26) for selectively turning the drum over a prescribed angular range.