  We consider bifurcation of solutions from a given trivial branch for a class
of strongly indefinite elliptic systems via the spectral flow. Our main results
establish bifurcation invariants that can be obtained from the coefficients of
the systems without using explicit solutions of their linearisations at the
given branch. Our constructions are based on a comparison principle for the
spectral flow and a generalisation of a bifurcation theorem due to Szulkin.
