  In extensions of the Standard Model with SU(2) singlet scalar fields, there
can be regions of parameter space for which the electroweak phase transition is
first order already at the mean-field level of analysis. We show that in this
case the phase interface (bubble wall) can become ultra-relativistic, with the
relativistic gamma factor gamma = (1-v_{wall}^2)^{-1/2} growing linearly with
the wall's propagation distance. We provide a simple criterion for determining
whether the bubble wall "runs away" in this way or if gamma approaches a
terminal value.
