  We take the first steps towards the complete computation of the
thermalization rate of the supersymmetric particles involved in electroweak
baryogenesis by computing the thermalization rate of the right-handed stop from
the imainary part of the two-point Green function. We use improved propagators
including resummation of hard thermal loops. The thermalization rate is
computed at the one-loop level in the high temperature approximation as a
function of $M_{\tilde t_R}(T)$. We also give an estimate for the magnitude of
the two-loop contributions which dominate the rate for small $M_{\tilde
t_R}(T)$. If the stop is non-relativistic with $M_{\tilde t_R}(T)\gg T$,
thermalization takes place by decay and is very fast.
