A separating apparatus for sheet material in which the sheet material is conveyed in stacks via a stack transporting system to a stack holder including a stack manipulator for effecting selective mechanical manipulation of the stack going through the separation process in the event that a deviation from the proper separation process is detected. In addition, a stack tester may be provided for testing the geometric and physical condition of the stack of sheet material before and during separation. An irregularity occurring during separation can be combatted by instituting a stack manipulation procedure which appears best suitable for automatically eliminating the disturbance of the separation process.