Abstract. A pseudosurface is a connected topological space resulting when finitely many identifications, of finetely many points each, are made on a finite collection of closed surfaces (=compact 2-manifolds). Any point obtained by such an identification of at least two distinct points is called a singular point.
A set of graphs is minor-closed if and only if it is closed under deletion of an edge or a vertex, and under contractoin of an edge. A surface S is minor-closed if and only if the set of graphs embeddable in S is minor-closed.
We prove that a pseudosurface S is minor-closed if and only if S consists of a pseudosurface S0, having at most one singular point, and some spheres glued to S0 in a tree structure.