This paper explores the local stability properties of the steady state in the two-sector neoclassical growth model. One sector produces consumption goods and the other sector produces the capital goods for both sectors and there are sector--specific externalities. We show analytically that if the capital goods for the two sectors are imperfect substitutes, then local indeterminacy near the steady state is impossible for every empirically plausible specification of the model parameters. More specifically, we show that a necessary condition for local indeterminacy is an upward-sloping aggregate labor demand curve in the capital sector, which requires an implausibly strong externality. We show numerically that an elasticity of substitution of plausible size implies determinacy near the steady state for all empirically plausible specifications of the other model parameters. These findings contrast sharply with the previous finding that local indeterminacy occurs in the two-sector model for a wide range of plausible parameter values when the two capital goods are perfect substitutes.