  In this work the spontaneous symmetry breaking in certain nonlinear theories
with second-class constraints is explored. Using the Dirac's method we perform
an analysis of the constraints and the counting of the degrees of freedom. The
corresponding effective Hamiltonian is constructed explicitly. It is shown that
on the surfaces where the effective Hamiltonian takes critical values the
symplectic structure becomes degenerate. In particular, we demonstrate that
under the condition of spontaneous symmetry breaking, which implies non trivial
vacuum surfaces, second-class constraints behave as first-class ones on certain
regions of the phase space, leading to undefined Dirac's brackets and to the
modification of the number of degrees of freedom. As a physical consequence,
these models can suffer from certain pathologies such as the existence of modes
with an acausal propagation. Concrete examples where this phenomena occurs are
described in detail.
