Abstract: In this paper, we introduce strongly power-serieswise McCoy
rings, which are a generalization of power-serieswise McCoy rings
and strongly McCoy rings, and investigate their properties. Let R
be a ring and I an ideal of R such that I is reduced, we show
that if R/I is strongly  power-serieswise McCoy(resp.,
power-serieswise McCoy), then R is strongly power-serieswise
McCoy(resp., power-serieswise McCoy). A ring R is power-serieswise
McCoy if and only if R[x] is power-serieswise McCoy. We find that
a class of strongly power-serieswise McCoy  rings of upper
triangular matrix ring over strongly  power-serieswise McCoy  rings.
Meanwhile, we show that power-serieswise Armendariz rings and
reduced rings are strongly power-serieswise McCoy rings.

Key words: McCoy ring, strongly McCoy ring, power-serieswise McCoy ring, strongly power-serieswise McCoy ring, upper triangular matrix ring