This chapter studies the analytical dynamic properties of a growing two-sector economy with Leontief sector technologies. After describing its structure and giving the conditions for full and efficient utilization of the production factors, it specifies the factor accumulation equations. In doing this, it shows that it is not necessary to model any specific saving behavior, as the Leontief technology, together with the assumptions of full and efficient factor utilization uniquely determines the output of the capital good sector and hence, investments, the gross capital accumulation flow. The analysis continues with the solution of the dynamic system and the investigation of its stability properties. An important contribution in this chapter is an illustration of the economic rationale behind the stability conditions. In order to appreciate the suggestions of these conditions, the chapter uses the so-called director function and shows the dynamics of the capital-labor ratio for alternative parameter constellations. The final part of the chapter extends the modeling framework to the case of endogenous labor supply, according to the standard assumption that the growth rate of the labor force depends on the level of per-capita consumption. The first published treatment of the two-sector growth model with sectoral fixed coefficients (Leontief) is due to Shinkai (Int Econ Rev 1:107–111, 1960).