  Roughly speaking, a conic bundle is a surface, fibered over a curve, such
that the fibers are conics (not necessarily smooth). We define stability for
conic bundles and construct a moduli space. We prove that (after fixing some
invariants) these moduli spaces are irreducible (under some conditions). Conic
bundles can be thought of as generalizations of orthogonal bundles on curves.
We show that in this particular case our definition of stability agrees with
the definition of stability for orthogonal bundles. Finally, in an appendix by
I. Mundet i Riera, a Hitchin-Kobayashi correspondence is stated for conic
bundles.
