Title: On Q-conic bundles Abstract: A 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. Jointly with Yuri Prokhorov, we study the structure of Q-conic bundles near their singular fibers. We show that the base surface of every Q-conic bundle has only Du Val singularities of type A (a positive solution of a conjecture by Iskovskikh). We obtain further the complete classification of Q-conic bundles under the additional assumption that the base surface is singular. Shigefumi Mori