In this paper, a graph G is two-disjoint-cyclecover r-pancyclic if for any integer l satisfying r ? l ? |V (G)|?r, there exist two vertex-disjoint cycles C1 and C2 in G such that the lengths of C1 and C2 are l and |V (G)|?l, respectively, where |V (G)| denotes the total number of vertices in G. Moreover, we define that a graph G is twodisjoint-cycle-cover edge r-pancyclic if for any two vertexdisjoint edges (u, v) and (x, y) of G, there exist two vertexdisjoint cycles C1 and C2 in G such that (i) C1 contains (u, v) with length l for any integer l satisfying r ? l ? |V (G)|?r, and (ii) C2 contains (x, y) with length |V (G)|?l. Then, we prove that the n-dimensional locally twisted cubes LTQn can be two-disjoint-cycle-cover 4-pancyclic for n ? 3 and two-disjoint-cycle-cover edge 2n-pancyclic for n ? 4.