W.P. Thurston introduced closed σ d-invariant laminations (where σ d = z d: S 1 → S 1, d ≥ 2) as a tool in complex dynamics. He defined wandering triangles as triples T ⊂ S 1 such that σ dn (T) consists of three distinct points for all n ≥ 0 and the convex hulls of all the sets σ dn (T) in the plane are pairwise disjoint, and proved that σ 2 admits no wandering triangles. We show that for every d ≥ 3 there exist uncountably many σ d-invariant closed laminations with wandering triangles and pairwise non-conjugate factor maps of σ d on the corresponding quotient spaces. © 2004 Académie des sciences. Published by Elsevier SAS. All rights reserved.