  Two-dimensional Maxwell-dilaton quantum gravity, which covers a large family
of the actions for two-dimensional gravity (in particular, string-inspired
models) is investigated. Charged black holes which appear in the theory are
briefly discussed. The one-loop divergences in the linear covariant gauges are
calculated. It is shown that for some choices of the dilaton potential and
dilaton-Maxwell coupling, the theory is one-loop multiplicatively
renormalizable (or even finite). A comparison with the divergences structure of
four-dimensional Einstein-Maxwell gravity is given.
