  I calculate the semiclassical phase shift ($\delta$), as function of impact
parameter ($b$) and velocity ($v$), when one D-brane moves past another. From
its low-velocity expansion I show that, for torroidal compactifications, the
moduli space of two identical D-branes stays flat to all orders in
$\alpha^\prime$. For K3 compactifications, the calculation of the D-brane
moduli-space metric can be mapped to a dual gauge-coupling renormalization
problem. In the ultrarelativistic regime, the absorptive part of the phase
shift grows as if the D-branes were black disks of area $\sim \alpha^\prime
ln{1\over 1-v^2}$. The scattering of large fundamental strings shares all the
above qualitative features. A side remark concerns the intriguing duality
between limiting electric fields and the speed of light.
