We study a multi-sector model of growth with differences in TFP growth rates across sectors and derive sufficient conditions for the coexistence of structural change, characterized by sectoral labor reallocation, and balanced aggregate growth. The conditions are weak restrictions on the utility and production functions commonly applied by macroeconomists. Per capita output grows at the rate of labor-augmenting technological progress in the capital-producing sector and employment moves to low-growth sectors. In the limit all employment converges to two sectors, the slowest-growing consumption-goods sector and the capital-goods sector.