  A $\mathbb Q$-conic bundle is a proper morphism from a threefold with only
terminal singularities to a normal surface such that fibers are connected and
the anti-canonical divisor is relatively ample. We study the structure of
$\mathbb Q$-conic bundles near their singular fibers. One corollary to our main
results is that the base surface of every $\mathbb Q$-conic bundle has only Du
Val singularities of type A (a positive solution of a conjecture by
Iskovskikh). We obtain the complete classification of $\mathbb Q$-conic bundles
under the additional assumption that the singular fiber is irreducible and the
base surface is singular.
