Let G be any compact connected Lie group and let T ≤ G be a maximal torus.  Then for any unstable Adams operation f of degree k, the following diagram commutes up to homotopy «!» And conversely, any map f that makes the above diagram commute must be an unstable Adams operation. Using this characterization, we will construct a self-map of a p-local compact group (S,F,L) in order to define unstable Adams operations on a more general setting. THEOREM.  For any p-local compact group (S,F,L) there is a self-equivalence such that the map on the objects when restricted to the identity component of S is a q^m-th power map.