  We give an overpartition analogue of Bressoud's combinatorial generalization
of the G\"ollnitz-Gordon theorem for even moduli in general case. Let
$\widetilde{O}_{k,i}(n)$ be the number of overpartitions of $n$ whose parts
satisfy certain difference condition and $\widetilde{P}_{k,i}(n)$ be the number
of overpartitions of $n$ whose non-overlined parts satisfy certain congruence
condition. We show that $\widetilde{O}_{k,i}(n)=\widetilde{P}_{k,i}(n)$ for
$1\leq i<k$.
