In the present paper the approach of the law of Thirlwall was used to study the relation between the economic growth and the external sector of Argentina in period 1970-2003. Thirlwall maintains that the main restriction that has an opened economy to obtain a rate of growth elevated in the long term is its balance of payments (BP). Strictly the restriction arises by the characteristics from the functions from demand by exports and imports. The law of Thirlwall indicates that if in the long term the rate of real growth of the GDP (yt) can be approximated through the rate of consistent growth with the balance of the BP (yb) and both are small in relation to third countries, then the growth of that economy this restricted by the BP. Empirically we worked first with the equation that relates to the GDP of Argentina and the World GDP through the ratio of the elasticities entrance of the demands by exports and imports, which defines the law of Thirlwall without flows of capitals. We demonstrated to the existence of a relation of long term between the GDP of Argentina and the world-wide GDP. We formalized the relation through the model TIME II. Soon one worked with the definition of the law of Thirlwall with real flows of capitals without getting to formulate a econometric model in as much we could not prove the existence of a relation of long term between the flows of real capitals and the GDP of Argentina between years 1970-2003. We changed the strategy and we studied the equations of demand by exports and imports. Through these we managed to calculate the elasticities income of both functions, that respectively turned out to be 2.02 and 3.41 for the exports and imports. Defining the ratio of elasticities entrance of the exports and imports (ε / π) equal to 0.59, minor to the unit. With this result we could calculate the rate of growth of the consistent GDP with the balance of the BP. The annual average of the considered rate was 2%, that approximates in the long term to the rate of real growth of the GDP equal to 1,9%. Both rates are smaller to experimented by regions and the countries in the same period. For example Brazil grew 4%, South America 3.1 and the world economy expanded to 3.1% annual. With these elements we can affirm that the growth of the GDP in Argentina during period 1970-2003 was restricted by the BP.