Several crucial features of dynamical symmetry breakdown (that is, without elementary scalar fields) cannot be fully understood from calculations of anomalous dimensions and linearized symmetry-breaking Dyson equations. In particular, the usual criterion of positive anomalous dimensions for the symmetry-breaking operators allows arbitrary $\mathrm{CP}$ violation in the linearized theory. It is also impossible at this level to determine all the parameters of the effective (Ginzburg-Landau) Lagrangian for composite Higgs fields. Instead, one must study the nonlinearities of the effective action in the dressed-loop expansion. We first show that, because the loop expansion of the effective action (sum of connected vacuum graphs) deals with dressed lines and vertices (skeletons with no self-energy insertions), it is possible to order the expansion in powers of the renormalized coupling constant, even though inverse powers of $g$ appear (signaling nonperturbative effects in the symmetry-breaking sector). Symmetric corrections to symmetry-breaking effects are ordered in positive powers of $g$. These results hold for both Abelian and non-Abelian gauge theories. Then we show that, for an Abelian gauge theory, $\mathrm{CP}$ violation does not occur at the level of two dressed loops in the effective action. We compute all masses and coupling constants appearing in he Ginzburg-Landau Lagrangian in terms of the coupling constants and masses of the symmetric theory, again at the two-loop level. A mass hierarchy appears, much like that of Coleman and Weinberg, in which the scalar mass is $O(g)$ times the vector mass.