In this paper, we focus on the stochastic (chaotic) attributes of the US dollar-based exchange rates for Brazil, Russia, India, China and South Africa (BRICS) using a long-run monthly dataset covering 1812M01-2017M12, 1814M01-2017M12, 1822M07-2017M12, 1948M08-2017M12, and 1844M01-2017M12, respectively. For our purpose, we consider the Lyapunov exponents, robust to nonlinear and stochastic systems, in both full - samples and in rolling windows. For comparative purposes, we also evaluate a long-run dataset of a developed currency market, namely British pound over the period of 1791M01-2017M12. Our empirical findings detect chaotic behavior only episodically for all countries before the dissolution of the Bretton Woods system, with the exception of the Russian ruble. Overall, our findings suggest that the establishment of the free floating exchange rate system have altered the path of exchange rates removing chaotic dynamics from the phenomenon, and hence, the need for policymakers to intervene in the currency markets for the most important emerging market bloc, should be carefully examined.