In the financial field, we are often faced with data that are somewhat non-linear. Thus, this research investigates the asymmetric behavior of the series through the Threshold Autoregressive and Momentum Threshold  asymmetry tests between price index using diary data between of the total price index of actions in stock markets of United States of America (S&P500) and Hong Kong (HANG SENG), from January 2, 1995 to March 29, 2013. With the empirical analysis it was possible to see the asymmetry in the series analysed through the TAR and M-TAR models. These oscillations demonstrate that behaviors are distinct in contractions and expansions.