This paper presents a dynamic small open economy version of the standard neoclassical exogenous growth model with international migration. It considers both the case of perfect world capital markets and the case of imperfect capital markets and shows that local indeterminacy always arises independently of the capital market regime. To study the dynamic implications of migration on domestic consumption, current account and capital accumulation, we simulate the model numerically by distinguishing three different scenarios depending on whether the initial immigration ratio is larger, equal or smaller than its steady-state value. In the case of perfect world capital markets, we find that migration has only a temporary impact on capital accumulation, but a permanent impact on domestic consumption and foreign debt. Instead, in the case of imperfect world capital markets, we find that migration has only temporary impacts on all the main macroeconomic variables.