For an extension $A;{subseteq};B$ of commutative rings, we present a sufficient conditio for the ring $[[A^{S,;leq}]]$ of generalized power series to be weakly normal (resp., stronglyt-closed) in $[[B^{S,;leq}]]$, where (S, $leq$) be a torsion-free cancellative strictly ordered monoid. As a corollary, it can be applied to the ring of power series in infinitely many indeterminates as well as in finite indeterminates.