A right -module is called -projective provided that it is projective relative to the right -module . This paper deals with the rings whose all nonsingular right modules are -projective. For a right nonsingular ring , we prove that is of finite Goldie rank and all nonsingular right -modules are -projective if and only if is right finitely - and flat right -modules are -projective. Then, -projectivity of the class of nonsingular injective right modules is also considered. Over right nonsingular rings of finite right Goldie rank, it is shown that -projectivity of nonsingular injective right modules is equivalent to -projectivity of the injective hull . In this case, the injective hull has the decomposition , where is projective and for each right ideal of . Finally, we focus on the right orthogonal class of the class of nonsingular right modules.