  In this paper, we present a detailed study of the problem of classical
stability of U(1) gauged Q-balls. In particular, we show that the standard
methods that are suitable for establishing the classical stability criterion
for ordinary (nongauged) one-field and two-field Q-balls are not effective in
the case of U(1) gauged Q-balls, although all the technical steps of
calculations can be performed in the same way as those for ordinary Q-balls. We
also present the results of numerical simulations in models with different
scalar field potentials, explicitly demonstrating that, in general, the regions
of stability of U(1) gauged Q-balls are not defined in the same way as in the
case of ordinary Q-balls. Consequently, the classical stability criterion for
ordinary Q-balls cannot be applied to U(1) gauged Q-balls in the general case.
