Neidhardt H., Zagrebnov V.A. On Error Estimates for the Trotter-Kato Product Formula. (42K, LATeX 209) ABSTRACT. We study the error bound in the operator-norm topology for the Trotter exponential product formula as well as for its generalization a la Kato. In the frame of the abstract setting we give a simple proof of error estimates which improve some recent results in this direction.