  We show that there are two classes of solutions that describe static
spherically symmetric dyonic dilaton black holes with two nonsingular horizons.
The first class includes only the already known solutions that exist for a few
special values of the dilaton coupling constant. Solutions belonging to the
second class have essentially different properties. They exist for continuously
varying values of the dilaton coupling constant, but arise only for discrete
values of the dilaton field at the horizon. For each given value of the dilaton
coupling constant, there may exist several such solutions differing by the
number of zeros of the shifted dilaton function in the subhorizon region and
separating the domains of singular solutions.
