  Let $R$ be a ring with identity, $(S,\leq)$ an ordered monoid, $\omega:S \to
End(R)$ a monoid homomorphism, and $A= R\left[\left[S,\omega \right]\right]$
the ring of skew generalized power series. The concepts of generalized Baer and
generalized quasi-Baer rings are generalization of Baer and quasi-Baer rings,
respectively. A ring $R$ is called generalized right Baer (generalized right
quasi-Baer) if for any non-empty subset $S$ (right ideal $I$) of $R$, the right
annihilator of $S^n \space{0.1cm}(I^n)$ is generated by an idempotent for some
positive integer $n$. Left cases may be defined analogously. A ring $R$ is
called generalized Baer (generalized quasi-Baer) if it is both generalized
right and left Baer (generalized right and left quasi-Baer) ring. In this
paper, we examine the behavior of a skew generalized power series ring over a
generalized right Baer (generalized right quasi-Baer) ring and prove that,
under specific conditions, the ring $A$ is generalized right Baer (generalized
right quasi-Baer) if and only if $R$ is a generalized right Baer (generalized
right quasi-Baer) ring.
