It is shown that periodic instanton solutions may have bifurcations wh
ich qualitatively change the behaviour of the finite temperature trans
ition rate. These bifurcations are studied numerically in a quantum me
chanical model and in the massive two-dimensional sigma model with the
Skyrme term. General rules which determine the behaviour of periodic
instantons near bifurcations are derived and applied to the Electrowea
k Theory. (C) 1997 Published by Elsevier Science B.V.