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 d n ( T ) consists of three distinct points for all n ⩾ 0 and the convex hulls of all the sets σ d n ( 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. To cite this article: A. Blokh, L. Oversteegen, C. R. Acad. Sci. Paris, Ser. I 339 (2004).