  The dynamics of symmetry breaking is an important issue in many branches of
physics including the real time onset of the Higgs-effect. In this thesis I
examine the linear and non-linear evolution of different systems in the broken
symmetric phase. The method of the analytical investigation is to derive
effective equations of motion for the soft modes of the theory. Numerical
investigation were performed for out-of-equilibrium classical systems. The
dynamics of the one-component scalar theory both in the linear-response
approximation and for large deviations from equilibrium is investigated. The
real time characterisation of the Goldstone effect when a condensate breaks the
O(N) symmetry of the quantum and classical field theory is given. The
corrections to the Hard Thermal Loop dynamics in the Abelian Higgs model, which
reflect the presence of the scalar condensate are calculated. An equation of
motion for the soft gauge field that incorporates the effect of the scalar
condensate is proposed to be used deep in the broken phase of the Abelian Higgs
model.
