This article examines the adaptive market hypothesis in the five most important Latin American stock indices. To that end, we apply three versions of the variance ratio test, as well as the Brock-Dechert-Scheinkman test for nonlinear predictability. Additionally, we perform the Dominguez-Lobato and generalized spectral tests to evaluate the Martingale difference hypothesis. Moreover, we consider salient news related to the plausible market inefficiencies detected by these four tests. Finally, we apply a GARCH-M model to assess the risk-return relationship through time. Our results suggest that the predictability of stock returns varies over time. Furthermore, the efficiency in each market behaves differently over time. All in all, the analyzed emerging market indices satisfy the adaptive market hypothesis, given the switching behavior between periods of efficiencies and inefficiencies, since the adaptive market hypothesis suggests that market efficiency and market anomalies might coexist in capital markets.