  The standard electroweak model is extended by means of a second
Brout-Englert-Higgs-doublet. The symmetry breaking potential is chosen is such
a way that (i) the Lagrangian possesses a custodial symmetry, (ii) a static,
spherically symmetric ansatz of the bosonic fields consistently reduces the
Euler-Lagrange equations to a set of differential equations. The potential
involves, in particular, products of fields of the two doublets, with a
coupling constant $\lambda_3$.Static, finite energy solutions of the classical
equations are constructed. The regular, non-trivial solutions having the lowest
classical energy can be of two types: sphaleron or bisphaleron, according to
the coupling constants. A special emphasis is put to the bifurcation between
these two types of solutions which is analyzed in function of the different
constants of the model,namely of $\lambda_3$.
