Let R be a ring, and let n, d be non-negative integers. A right R-module M is called (n, d)-projective if Ext d+ 1 R (M, A)= 0 for every n-copresented right R-module A. R is called right n-cocoherent if every n-copresented right R-module is (n+ 1)-copresented, it is called a right co-(n, d)-ring if every right R-module is (n, d)-projective. R is called right n-cosemihereditary if every submodule of a projective right R-module is (n, 0)-projective, it is called a right nV-ring if it is a right co-(n, 0)-ring. Some properties of (n, d)-projective modules and (n, d)-projective dimensions of modules over n-cocoherent rings are studied. Certain characterizations of n-copresented modules,(n, 0)-projective modules, right n-cocoherent rings, right n-cosemihereditary rings, as well as right nV-rings are given respectively.