  In the unitary gauge the unphysical degrees of freedom of spontaneously
broken gauge theories are eliminated. The Feynman rules are simpler than in
other gauges, but it is non-renormalizable by the rules of power counting. On
the other hand, it is formally equal to the limit $\xi \to 0$ of the
renormalizable R$_{\xi}$-gauge. We consider perturbation theory to one-loop
order in the R$_{\xi}$-gauge and in the unitary gauge for the case of the
two-dimensional abelian Higgs model. An apparent conflict between the unitary
gauge and the limit $\xi \to 0$ of the R$_{\xi}$-gauge is resolved, and it is
demonstrated that results for physical quantities can be obtained in the
unitary gauge.
