Abstract: Let R be an associative ring with identity and X is a class that contains all flat R-modules, the definitions of X-Ding projective modules and X-Ding projective dimensions are introduced and the relative properties are studied. A right R-module M is called X-Ding projective if there exists an exact sequenceP=∶…→P₁→P₀→P⁰→P¹→…of projective right R-modules such that M=Ker (P⁰→P¹) andHom_R(P,F) is exact whenever F∈X. It is proved that the class of all X-Ding projective modules is projectively resolving and is closed under direct sums and direct summands. In addition, it is proved that ifGX-Dpd(R)<∞,then (X-DP(R), (X-DP(R))^⊥) is a complete here ditary cotorsion pair.

Key words: X-Ding projective module, X-Ding projective dimension, cotorsionpair