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This paper deals with singular perturbation problems for vector flelds on 2-dimensional manifolds. \Canard solutions" are solutions that, start- ing near an attracting normally hyperbolic branch of the singular curve, cross a \turning point" and follow for a while a normally repelling branch of the singular curve. Following the geometric ideas developed in (DR) for the study of canard solutions near a generic turning point, we study canard solutions near non-generic turning points. Characterization of manifolds of canard so- lutions is given in terms of boundary conditions, their regularity properties are studied and the relation is described with the more traditional asymptotic approach. It reveals that interesting information on canard solutions can be obtained even in cases where an asymptotic approach fails to work. Since the manifolds of canard solutions occur as intersection of center manifolds deflned along respectively the attracting and the repelling branch of the singular curve, we also study their contact and its relation to the \control curve".

Canard solutions at non-generic turning points