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A hypothesis that has been examined is convergence which was introduced by Baumol (1986) and Abramovitz (1986). Barro and Sa1a-I-Martin (1991,1992, 1995) examined two kinds of convergence: (I) Absolute Beta-convergence means higher real per capita income growth for regions with lower initial per capita income when regions (or countries) are the same in their growth path parameters, Conditional Beta-convergence means higher per capita income growth for regions with lower initial per capita income after accounting for differences in regional growth path parameters; Sigma-convergence means the reduction of regional per capita income variance with the passage of time. The main contribution of this paper is the examination of convergence by using the data on demand deposits of Iran's provinces for the time period 13691379(1990-2000) on the basis of endogenous money supply theory in both RBC and Post-Keynesian traditions. Our findings do not support Beta and Sigmaconvergence in Iran's provinces.