In this paper we are interested in studying the properties of Armendariz, Baer, quasi-Baer, p.p. and p.q.-Baer over skew PBW extensions. Using a notion of compatibility, we generalize several propositions established for Ore extensions and present new results for several noncommutative rings which can not be expressed as Ore extensions (universal enveloping algebras, diffusion algebras, and others).