  Let R be a ring with identity, (M;\leq) a commutative positive strictly
ordered monoid and w_m an automorphism for each m \in M . The skew generalized
power series ring R[[M,w]] is a common generalization of (skew) polynomial
rings, (skew) power series rings, (skew) Laurent polynomial rings, (skew) group
rings, and Mal'cev Neumann Laurent series rings. If S\subset R is a
multiplicative set, then R is called right S-Noetherian, if for each ideal I of
R, Is \subseteq J\subseteq I for some s\in S and some finitely generated right
ideal J . Unifying and generalizing a number of known results, we study
transfers of S-Noetherian property to the ring R[[M,w]]. We also show that the
ring R[[M,w]] is left Noetherian if and only if R is left Noetherian and M is
finitely generated. Generalizing a result of Anderson and Dumitrescu, we show
that,when S\subset R is a-anti-Archimedean multiplicative set with a an
automorphism of R, then R is right S-Noetherian if and only if the skew
polynomial ring R[x,a] is right S-Noetherian.
