Abstract: A new set of invariants was defined for right-invertible nonlinear control systems,the right essential orders. We prove that this set of natural numbers is invariant under regular static state feedbacks. On the other hand, it is pointed by an example that the right essential orders are changeable by regular dynamic state feedbacks. Some application of the right essential orders to the decoupling problem is addressed. Especially, a new necessary and sufficient condition is obtained via the right essential orders for the regular feedback decoupling problem of nonlinear systems. The relation between the right essential orders and the nonlinear Morgan's problem is also discussed. It is expected that the invariants introduced here plays an important role in the study of nonlinear Morgan' s problem.