Some properties of charged, black hole solutions of two-dimensional string inspired gravity are presented. These black holes have the same causal structure as the Reissner--Nordström solution of general relativity and exhibit a similar instability of the inner horizon. A generic perturbation, by a two-dimensional scalar field, transforms the horizon into a curvature singularity. We investigate semiclassical effects near to this singularity. The calculations suggest that the curvature diverges more strongly in the presence of quantized matter fields. Our results are then contrasted with four-dimensional estimates.