  Continuum models with critical end points are considered whose Hamiltonian
${\mathcal{H}}[\phi,\psi]$ depends on two densities $\phi$ and $\psi$.
Field-theoretic methods are used to show the equivalence of the critical
behavior on the critical line and at the critical end point and to give a
systematic derivation of critical-end-point singularities like the thermal
singularity $\sim|{t}|^{2-\alpha}$ of the spectator-phase boundary and the
coexistence singularities $\sim |{t}|^{1-\alpha}$ or $\sim|{t}|^{\beta}$ of the
secondary density $<\psi>$. The appearance of a discontinuity eigenexponent
associated with the critical end point is confirmed, and the mechanism by which
it arises in field theory is clarified.
