Given positive integers r" r2, r¡,..., r¡ such that r¡ < r2 < r} < ■ ■ ■ < rj < m; m > 1 ; we find the number P(n, m; R)o( partitions of a given positive integer n into parts belonging to the set R of residue classes ri(modm), r2 (mod m),..., rj (mod m). This leads to an identity which is more general though less elegant then the well-known Rogers-Ramanujan identities.