  We show that surface solitons form continuous families in one-dimensional
complex optical potentials of a certain shape. This result is illustrated by
non-Hermitian gap-surface solitons at the interface between a uniform
conservative medium and a complex periodic potential. Surface soliton families
are parameterized by a real propagation constant. The range of possible
propagation constants is constrained by the relation between the continuous
spectrum of the uniform medium and the band-gap structure of the periodic
potential.
