  We construct the consistent supersymmetric extensions of the operators
describing the recoil of a D-brane and show that they realize an N=1
logarithmic superconformal algebra. The corresponding supersymmetric vertex
operator is related to the action of a twisted superparticle with twist field
determined by the angular momentum of the recoiling D-brane and with explicitly
broken kappa-symmetry. We show that the superconformal completion removes the
logarithmic modular divergences that are present in the bosonic string loop
scattering amplitudes. These features are all consequences of the relationship
that exists in these models between worldsheet rescaling and the time evolution
of the D-brane in target space.
