There is a family of models with physical and human capital and R&D for which convergence properties have been discussed [Lutz G. Arnold, European Economic Review 44, 1599-1605 (2000); Manuel Gomez, Studies in Nonlinear Dynamics and Econometrics 9(1), Article 5 (2005)]. However, spillovers in R&D have been ignored in this context. We introduce spillovers in this model and derive the steady-state and stability properties. This new feature implies that the model is characterized by a system of four differential equations. A unique balanced growth path, along with a two-dimensional stable manifold, is obtained under simple and reasonable conditions. Transition is oscillatory toward the steady state for plausible values of parameters. We discovered that these features are due to the presence of the R&D spillovers externality in the decentralized equilibrium.