  It was found in the two-dimensional quantum gravity both in the de Donder
gauge and in the lightcone gauge that one of field equations breaks down at the
level of the representation, though the breakdown is very little. It is shown
that this anomalous behavior occurs also in a very simple model analogous to
the lightcone-gauge two-dimensional quantum gravity. This model, however, can
be transformed into a free field theory by a nonsingular transformation. Of
course, the latter has no anomaly. The cause of the discrepancy is analyzed.
