This paper is a continuation of the papers J. Pure Appl. Algebra, 210 (2007), 437--445 and J. Algebra Appl., 8 (2009), 219--227. Namely, we introduce and study a doubly filtered set of classes of modules of finite Gorenstein projective dimension, which are called (n,m)-strongly Gorenstein projective ((n,m)-SG-projective for short) for integers n≥1 and m≥0
Nearby in the stack
. We are mainly interested in studying syzygies of these modules. As consequences, we show that a module
M
has Gorenstein projective dimension at most
m
if and only if
M⊕G
is
(1,m)
-SG-projective for some Gorenstein projective module
G
. And, over rings of finite left finitistic flat dimension, that a module of finite Gorenstein projective dimension has finite projective dimension if and only if it has finite flat dimension.