In this note we will be concerned with the proof and consequences of the following fact : if o is a differentiate action of a compact Lie group on a compact differentiate manifold M, then any differentia t e action of G on M sufficiently close to 0o in the C^topology is equivalent to 0O. 1. Notation. In what follows differentiate means class C. If M and V are differentiate manifolds, 2HI(M, ...