Given two pairs 〈u, v〉 and 〈x, y〉 of vertices of a graph G=(V,E) and two integers l1 and l2 with l1+l2=|V(G)|−2, G is said to be satisfying the 2RP-property if there exist two disjoint paths P1 and P2 such that (1) P1 is a path joining u to v with l(P1)=l1, (2) P2 is a path joining x to y with l(P2)=l2, and (3) P1∪P2 spans G, where l(P) denotes the length of path P. In this paper, we show that an r-dimensional generalized hypercube, denoted by G(mr,mr−1,…,m1), satisfies the 2RP-property except some special conditions, where mi⩾4 for all 1⩽i⩽r.