  We develop relative oscillation theory for one-dimensional Dirac operators
which, rather than measuring the spectrum of one single operator, measures the
difference between the spectra of two different operators. This is done by
replacing zeros of solutions of one operator by weighted zeros of Wronskians of
solutions of two different operators. In particular, we show that a Sturm-type
comparison theorem still holds in this situation and demonstrate how this can
be used to investigate the number of eigenvalues in essential spectral gaps.
Furthermore, the connection with Krein's spectral shift function is
established. As an application we extend a result by K.M. Schmidt on the
finiteness/infiniteness of the number of eigenvalues in essential spectral gaps
of perturbed periodic Dirac operators.
