This paper shows that the Romer (1990) Journal of Political Economy, 98, 71-102 model of endogenous growth, its version for the social planning problem, has a unique steady state and is saddle path stable. The steady state can be monotonically reached by an appropriate choice of the initial values of the control variables if the initial values of the state variables lie in the vicinity of the steady state. For the original version, as well as for generalizations of it, we demonstrate that Hopf bifurcation can be excluded. We also demonstrate that the market variant of the Romer model as, for example, presented in Benhabib, Peru and Xie (1994) Ricerche Economiche, 48, 279-298, does admit Hopf bifurcation and stable periodic solutions. The technique employed here may be useful in studying other variants of endogenous growth models. © 1998 Academic Press Limited.