A method is proposed for measuring thickness and detecting double and missing sheets during the sheet feed to a sheet-processing machine, such as a sheet-fed printing machine. A corresponding monitoring apparatus has one or more sensing elements above or beneath the sheet stream. The sensing element can be displaced, with an actuating device having an actuating drive, in the direction towards and away from the sheet stream. The actuating drive has at least one piezoelectric actuator or it is formed by the latter.