  Let $R$ be a ring, $(S,\leq)$ a strictly ordered monoid and $\omega:
S\rightarrow End(R)$ a monoid homomorphism. In this paper we study the
ascending chain conditions on principal left (resp. right) ideals of the skew
generalized power series ring $R[[S,\omega ]]$. Among other results, it is
shown that $R[[S,\omega ]]$ is a right archimedean reduced ring if $S$ is an
Artinian strictly totally ordered monoid, $R$ is a right archimedean and
$S$-rigid ring which satisfies the ACC on annihilators and $\omega_s$ preserves
nonunits of $R$ for each $s\in S$. As a consequence we deduce that the power
series rings, Laurent series rings, skew power series rings, skew Laurent
series rings and generalized power series rings are reduced satisfying the
ascending chain condition on principal left (or right) ideals. It is also
proved that, the skew Laurent polynomial ring $R[x,x^{-1};\alpha]$ satisfies
\emph{ACCPL(R)}, if $R$ is $\alpha$-rigid and satisfies \emph{ACCPL(R)} and the
$ACC$ on left(resp. right) annihilators. Examples are provided to illustrate
and delimit our results.
