In this paper, it is shown that if a nonlinear system admits a Lie symmetry that can be transformed into its Poincare-Dulac normal form by a state diffeomorphism, then, under some technical conditions, such a nonlinear system can be immersed into a linear one. This allows us to compute in closed-form the flow, all algebraic invariant curves (through semi-invariants) of the nonlinear system, and Lyapunov functions to study stability properties. (C) 2009 Elsevier Ltd. All rights reserved.