In a sheet-processing apparatus, banknotes are separated by a separator (10) and fed to a depositing arrangement (18) via a sensor and transporting unit (8). Depositing takes place in different depositing compartments in accordance with depositing criteria which are determined by certain features of the banknotes (BN) being sensed. The individual depositing compartments (30, 32, 34) of the depositing arrangement (18) are assigned stacker wheels (20, 22, 24), which have stacker fingers which, in pairs, define a sheet compartment between them. The banknotes are introduced into the sheet compartments and are then deposited in the associated depositing compartment by the stacker fingers. In order to prevent fed banknotes from coming into contact with stacker-finger tips and then not being deposited correctly, the rotational speed (including phase) of the stacker wheels (20, 22, 24) is synchronized with the operating frequency of the separator (10) such that the individual banknotes enter centrally into the sheet compartments of the stacker wheels.