  I give explicit fromulae for full propagators of vector and scalar fields in
a generic spin-1 gauge model quantized in an arbitrary linear covariant gauge.
The propagators, expressed in terms of all-order one-particle-irreducible
correlation functions, have a remarkably simple form because of constraints
originating from Slavnov-Taylor identities of Becchi-Rouet-Stora symmetry. I
also determine the behavior of the propagators in the neighborhood of the
poles, and give a simple prescription for the coefficients that generalize (to
the case with an arbitrary vector-scalar mixing) the standard
$\sqrt{\mathcal{Z}}$ factors of Lehmann, Symanzik and Zimmermann. So obtained
generalized $\sqrt{\mathcal{Z}}$ factors, are indispensable to the correct
extraction of physical amplitudes from the amputated correlation functions in
the presence of mixing. The standard $R_\xi$ guauges form a particularly
important subclass of gauges considered in this paper. While the tree-level
vector-scalar mixing is, by construction, absent in $R_\xi$ gauges, it
unavoidably reappears at higher orders. Therefore the prescription for the
generalized $\sqrt{\mathcal{Z}}$ factors given in this paper is directly
relevant for the extraction of amplitudes in $R_\xi$ gauges.
