  In this paper, we prove that for a $n$-perfect ring $R$ various classes of
relative Gorenstein projective $R$-modules are special precovering, among them
including the Gorenstein projectives and Ding projectives. Also we prove that
the class of projectively coresolved Gorenstein flat $\mathcal{PGF} (R)$
fulfils the same feature. We also introduce a new class of Gorenstein
projective $R$-modules relative to the Auslander class $\mathcal{A} _{C} (R)$
of a semidualizing $(R,S)$-bimodule $_R C_S$.
