This papers estimates unrestricted monetary reaction functions for four Latin American countries (Brazil, Chile, Colombia and Mexico) and tests for the presence of non-linear effects in central bank behaviour. The analysis covers the post-1999 inflation-targeting period. We deal with the presence of unit roots in the data by estimating the policy rules in a co-integration setting. We test for linear and non-linear co-integration among the variables of interest. The results suggest that a non-linear specification is not rejected by the data for Brazil, Colombia and Mexico, but it is for Chile. Estimation of smooth-transition models by NLLS and EN-NLLS suggests that the central bank's response to the inflation gap (i.e. deviations of expected inflation from the target) is invariant across policy regimes in Colombia. It becomes stronger in Mexico as expected inflation deviates from the target. Policy responses appear to weaken in Brazil as the inflation gap widens, a finding that most probably reflects a history of adverse supply shocks and upward adjustments in targets in the early years of inflation targeting. Non-linearity is also found in the central bank's response to the exchange rate in Brazil and Colombia.