Let Aut(Un) denote the automorphism group of the polydisk Unin Cn. u denotes the subgroup of Aut(Un) consisting of linear automorphisms. A subspace Y of C(Tn) is Mobius invariant if [f φ: f;εY, φε Aut(Un)] ⊂Y. (Invariance of Y w.r.t. u (or a single automorphism) is defined similarly.) In this paper, we show that a u-invariant closed subspace C(Tn) is Möbius invariant iff it is invariant w.r.t. an automorphism not in u. We show that there are exactlyMöbius invariant closed subspaces in C(Tn). Similar results are proved forFurther. we find all Möbius invariant closed subspaces of C(T2).