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The non-perturbative structure of the photon and gluon propagators plays animportant role in governing the dynamics of quantum electrodynamics (QED) andquantum chromodynamics (QCD) respectively. Although it is often assumed thatthese interacting field propagators can be decomposed into longitudinal andtransverse components, as for the free case, it turns out that in general thisis not possible. Moreover, the non-abelian gauge symmetry of QCD permits themomentum space gluon propagator to contain additional singular terms involvingderivatives of $\delta(p)$, the appearance of which is related to confinement.Despite the possibility of the failure of the transverse-longitudinaldecomposition for the photon and gluon propagators, and the appearance ofsingular terms in the gluon propagator, the Slavnov-Taylor identitynevertheless remains preserved.