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In this paper, we study the action on C^n of any group G of holomorphicdiffeomorphisms (automorphisms) of C^n fixing 0. Suppose that there is x inC^n, having an orbit which generates C^n and also E(x)=C^n, where E(x) is thevector space generated by L_{G}={D_{0}fx, f in G }. We give an importantcondition so that an orbit G(x) is isomorphic (by linear map) to the orbitL_{G}(x)of the linear group L_{G}. More if G is abelian, we prove the existenceof a G-invariant open set U, dense in C^n, in which every orbit O is relativelyminimal (i.e. the closure of O in U is a closed non empty, G-invariant set andhas no proper subset with these properties). Moreover, if G has a dense orbitin C^n then every orbit of U is dense in C^n.

On the dynamic of holomorphic diffeomorphisms groups fixing a commune point, on C^n