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The main aim of this paper is to verify the dynamic interdependence and transmission of volatility from the American (SP500) to the Brazilian stock market (IBOVESPA and sectoral indexes). Estimates were performed by GARCH/BEKK methodology, considering the period from January 2007 to December 2019. In the periods considered as "critical events" there was a significant increase in the conditional covariance between SP500 and Brazilian stock indexes (IBOVESPA and sector indices), which suggests for the hypothesis of financial contagion. The covariance increased more intensely and persistently during the so-called subprime crisis, one that had a major impact on the Brazilian economy, especially for the financial and industrial indexes. Furthermore, conditional variance estimates for Brazilian indexes revealed that that internal turmoil, whether economic or political, regardless of the international scenario ("critical events"), affected the volatility of the Brazilian stock market. These results have important implications regarding the future decisions of economic agents (politicians and investors), contributing to a better understanding of the behavior of the Brazilian stock market vis-à-vis the American stock market and the internal turbulences in the Brazilian economy, whether political or economic.