The study of the asymmetric behavior of macroeconomic variables over the business cycles phases has had a long tradition in economics. In this work we find evidence in favor of the hypothesis of having a Star-type nonlinear asymmetric behavior of the economy activity, over the last two decades, in four Latin American countries: Brazil, Chile, Colombia and Mexico. For Venezuela the null hypothesis of a linear process could not be rejected under the method placed by Granger and Terasvirta (1993). Economic activity is proxies by monthly based industrial production indexes. Except for the case of Mexico, we arrive to asymmetric representations of the processes. However, evidence of asymmetric behavior is found according to the impulse response function analysis for all the countries.