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Two-dimensional Maxwell-dilaton quantum gravity, which covers a large familyof the actions for two-dimensional gravity (in particular, string-inspiredmodels) is investigated. Charged black holes which appear in the theory arebriefly discussed. The one-loop divergences in the linear covariant gauges arecalculated. It is shown that for some choices of the dilaton potential anddilaton-Maxwell coupling, the theory is one-loop multiplicativelyrenormalizable (or even finite). A comparison with the divergences structure offour-dimensional Einstein-Maxwell gravity is given.Comment: UB-ECM-PF 92/17, Latex file, 12 page

ONE-LOOP DIVERGENCES IN TWO-DIMENSIONAL MAXWELL-DILATON QUANTUM GRAVITY