We reconsider some families of orthogonal polynomials, within the framework of the so called monomiality principle. We show that the associated operational formalism allows the framing of the polynomial orthogonality using an algebraic point of view. Within such a frame- work, we introduce families of pseudo-orthogonal polynomials, namely polynomials, not orthogonal under the ordinary denition, but provid- ing series expansions, which can be obtained from the ordinary series using the monomiality correspondence.