Abstract: In this paper we consider the observability problem for a particular class of nonlinear systems on Lie groups that we called automorphisms control systems, in wich, every associated vector fields induces a one parameter groups of automorphisms of the state space. Such systems generalizes the so called bilinear systems wich are useful to approximate a large class of nonlinear systems and the result of this work characterize the observability of the direct product of automorphisms control systems wich is closely related with that sort of approximation Ver menos