W.P. Thurston introduced closed σd-invariant laminations (where σd = zd: S1 → S1, d ≥ 2) as a tool in complex dynamics. He defined wandering triangles as triples T ⊂ S1 such that σdn (T) consists of three distinct points for all n ≥ 0 and the convex hulls of all the sets σdn (T) in the plane are pairwise disjoint, and proved that σ2 admits no wandering triangles. We show that for every d ≥ 3 there exist uncountably many σd-invariant closed laminations with wandering triangles and pairwise non-conjugate factor maps of σd on the corresponding quotient spaces. © 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved.