  In 1967, Andrews found a combinatorial generalization of the
G\"ollnitz-Gordon theorem, which can be called the Andrews-G\"ollnitz-Gordon
theorem. In 1980, Bressoud derived a multisum Rogers-Ramanujan-type identity,
which can be considered as the generating function counterpart of the
Andrews-G\"ollnitz-Gordon theorem. Lovejoy gave an overpartition analogue of
the Andrews-G\"ollnitz-Gordon theorem for $i=k$. In this paper, we give an
overpartition analogue of this theorem in the general case. By using Bailey's
lemma and a change of base formula due to Bressoud, Ismail and Stanton, we
obtain an overpartition analogue of Bressoud's identity. We then give a
combinatorial interpretation of this identity by introducing the
G\"ollnitz-Gordon marking of an overpartition, which yields an overpartition
analogue of the Andrews-G\"ollnitz-Gordon theorem.
