We analyze the effective three-dimensional theory previously construct
ed for the MSSM and multi-Higgs models to determine the regions of par
ameter space in which the electroweak phase transition is sufficiently
strong for a B + L asymmetry to survive in the low-temperature phase.
We find that the inclusion of all supersymmetric scalars and all one-
loop corrections has the effect of enhancing the strength of the phase
transition. Without a light stop or extension of the MSSM the phase t
ransition is sufficiently first order only if the lightest Higgs mass
M-h less than or similar to 70 GeV and tan beta less than or similar t
o 1.75. (C) 1997 Published by Elsevier Science B.V.