This paper deals with endogenous growth and human capital accumulation. We present a review of previous studies, particularly stressing the distinction between rival and non-rival uses of human capital. Our own model in section 2 is based on Lucas 1988 model of human capital, and it modifies the way human capital is accumulated, by using a Cobb-Douglas production function, in which physical investments in education are added to the usual arguments considered by the literature. The framework is a dynamic intertemporal maximization in which agents can allocate time between working, leisure and accumulation of human capital. If the fraction of capital devoted to education is made function of time, we obtain three results. First: increasing investment in human capital has a double positive effect on growth, whereas taking away resources from education to physical capital has a double negative effect. Second: the elasticity of these increases depends crucially on the internal productivity of human capital, that is, how much human capital stock today is important for the production of human capital tomorrow; this is in line with those studies who denies the conditional convergence predicted by exogenous growth models. Third: in steady state, human capital can grow faster than physical capital in competitive equilibrium, if the magnitude of the external effect is offset by the effect caused by the increase of the investment in education (which in turn depends crucially on the elasticity).