Growth models often give rise to saddle-point stable dynamic systems with multi-dimensional stable manifolds. It is argued that standard solution procedures used to numerically approximate the transition process are generally inadequate when the (stable) eigenvalues differ substantially in magnitude. Therefore, the relaxation procedure is proposed as a powerful method for simulating the transition process in dynamic macroeconomic models. We argue that this procedure is in general well-suited and highly efficient. The procedure can be easily applied to dynamic systems which exhibit the above mentioned structural characteristics. This is demonstrated by simulating the transition process of the well-known Jones (1995) model.