  The existence of gravitational anomalies claimed by Alvarez-Gaume and Witten
is examined critically. It is pointed out that they were unaware of the
essential difference between T-product quantities and T*-product quantities.
Field equations and, therefore, the Noether theorem are, in general, violated
in the case of T*-product quantities, that is, those directly calculable from
Feynman integrals. In the 2-dimensional case, it is explicitly confirmed that
the energy-momentum tensor is strictly conserved if the above stated property
of the T*-product quantities is correctly taken into account. The non-existence
of gravitational anomalies is explicitly demonstrated for the BRS-formulated
2-dimensional quantum gravity in the Heisenberg picture.
