We construct a dilatonic two-dimensional model of a charged black hole. The
classical solution is a static charged black hole, characterized by two pa
rameters in and q representing the black hole's mass and charge. Then we st
udy the semiclassical effects, and calculate the evaporation rate of both m
and q, as a function of these two quantities. Analyzing this dynamical sys
tem, we find two qualitatively different regimes, depending on the electrom
agnetic coupling constant g(A). If the latter is greater than a certain cri
tical value, the charge-to-mass ratio decays to zero upon evaporation. On t
he other hand, for g(A) smaller than the critical value, the charge-to-mass
ratio approaches a non-zero constant that depends on g(A) but not on the i
nitial values of m and q.