We use the boundary state formalism to study the interaction of two moving identical D-branes in the Type II superstring theory compactified on orbifolds. By computing the velocity dependence of the amplitude in the limit of large separation we can identify the nature of the different forces between the branes. In particular, in the Z(3) orbifold case we find a boundary state which is coupled only to the N = 2 graviton multiplet containing just a graviton and a vector like in the extremal Reissner-Nordstrom configuration. We also discuss other cases including T-4/Z(2). (C) 1997 Elsevier Science B.V.