A regular semigroup S is said to be quasi-orthodox if there exist an inverse semigroup Г with basic semilattice Λ (that is, Λ is the semilattice of idempotents of Γ) and a surjective homomorphism f: S→Γ such that λf^<-1> is a completely simple subsemigroup of S for each λ∈Λ. In this paper, the structure of quasi-orthodox semigroups is studied.