  In this paper, we study the relation between $m$-strongly Gorenstein
projective (resp. injective) modules and $n$-strongly Gorenstein projective
(resp. injective) modules whenever $m \neq n$, and the homological behavior of
$n$-strongly Gorenstein projective (resp. injective) modules. We introduce the
notion of $n$-strongly Gorenstein flat modules. Then we study the homological
behavior of $n$-strongly Gorenstein flat modules, and the relation between
these modules and $n$-strongly Gorenstein projective (resp. injective) modules.
