In this study we examine productivity growth and their relationship with international openness in Latin American countries over the period 1980-2006. Overall results on productivity indicate a stagnation process for the entire period 1986-2006. The decomposition of productivity into catching up and technical change reveals that the first have a stagnation process and the latter worsening. Analyzing the relationship between productivity growth and international openness we find different patterns for both methodologies parametric (Arellano-Bond estimator) and nonparametric (GAM) and for both measures of international openness merchandise trade (% of GDP) and (export+imports)/GDP. In particular in a parametric way, although the shape is curvilinear for both models the relationship is positive inverted U-shaped in the first case and Ushaped in second.