This short paper analyzes the dynamic relationship between air transportation and economic growth in four South American countries, Argentina, Brazil, Chile and Uruguay, investigating the linkages without imposing a priori any parametric model to represent them. A set of free-model tests (unit root, cointegration and causality non-parametric tests) are applied to annual data (from 1970 to 2015) of per capita GDP and air transport indicators (passengers and cargo) to examine the existence of linear and nonlinear relationships between these variables. Real exchange rate is introduced in each country model in order to account for the price-effects. Results show that only Uruguay and Chile show a cointegration relationship between economic growth and air transport (and when number of air passengers represents this variable). Linearity (of the long-run relationship) was rejected for both countries, which means that the relationship between air transport and growth may have some kind of asymmetry or non-linear behavior. Nor for Argentina or Brazil and neither when air transport is represented by air cargo indicator, cointegration was found. Furthermore, nonparametric causality tests, confirm bidirectional causality from air transport to growth in Uruguay and Chile.