Two definitions of a proximity base and subbase have been given, one by A. Csasar and S. Mrowka [1] and the other by O. Njastad [7], but neither of these definitions is perfectly satisfactory. In [8], P. L. Sharma introduced a new definition of proximity base and subbase removing the fault that the previous definitions had had. In this paper we shall show that the notion of proximity base and subbase can be introduced in the spaces of $R$-proximity in a similar way.