Abstract
Locally conformal almost quasi-Sasakian manifolds set up a wide class of almost contact metric manifolds containing several interesting subclasses. Contact-complex Riemannian submersions whose total space belongs to each of the considered classes are studied. In particular, the Chinea-Gonzalez class of the fibres and the Gray-Hervella class of the base space are related. The main properties of the O'Neill invariants are stated. This allows discussing the integrability of the horizontal distribution and the minimality of the fibres.