AbstractWe say that a graph family ℱ has the Erdös‐Pósa property if there exists a functionf(k) such that any graphGcontains eitherkdisjoint subgraphs each isomorphic to a member of ℱ, or contains a setSof at mostf(k) vertices such thatG — Scontains no graph in ℱ. We derive a general sufficient condition for a family of graphs to have the Erdös‐Pósa property. In particular, for any fixed natural numbermthe collection of cycles of length divisible bymhas the Erdös‐Pósa property. As a by‐product, we obtain a polynomially bounded algorithm for finding a cycle of length divisible bym. On the other hand, we describe a general class of planar graphsHsuch that a collection of subdivisions ofHdoes not have the Erdös‐Pósa property. In