We study spin interactions between two moving D-branes using the Green-Schwarz formalism of boundary states. We focus our attention on the leading terms for small velocities v, of the form v(4-n)/r(7-P+n) (v(2-n)/r(3-p+n)) for p-p (p-p + 4) systems, with 16 (8) supercharges. In analogy with standard GS computations of massless four-point one-loop amplitudes in Type I theory, the above terms are governed purely by zero-modes, massive states contributions cancelling as expected by the residual supersymmetry. This implies the scale invariance of these leading spin effects, supporting the relevant matrix model descriptions of supergravity interactions; in this context, we also discuss similar results for more general brane configurations. We then give a field theory interpretation of our results that allows us in particular to deduce the gyromagnetic ratio g = 1 and the presence of a quadrupole moment for D0-branes. (C) 1998 Elsevier Science B.V.