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Long-run relationships and structural breaks have often been confused so that many investigators ignore the structural breaks in long-run stock price relationships. In this paper, we investigate the long-run relationships among stock prices in BRICS countries in a bivariate framework. We used a non-linear threshold cointegration test, which endogenously incorporates possible regime shift behaviors into the long-run relationships from 2004 to 2018. The Johansen cointegration test, the Gregory and Hansen cointegration test, and the Hatemi-J regime shift cointegration test, which allow for single and double structural breaks, were used. The principal finding of this paper confirms the presence of cointegration among the BRICS stock markets with two endogenous structural breaks. The study confirms that ignoring the presence of structural breaks in long-run series data can produce ambiguous results. It also confirms the absence of cointegration among these stock markets (Brazil and China, India and China, and China and South Africa) after two endogenous structural breaks. These empirical findings support conjecture on more than just the changes in the relationships between the BRICS stock markets. The disintegrated markets suggest the absence of arbitrage activity and vice versa. Thus, disintegrated markets mean that investors can obtain long-term gains through international portfolio diversification. While the benefit of the diversification is very limited in the long run, it is unlikely to be eliminated in practice. Hence, there is a possibility of obtaining an unusual profit in such a market, and consequently the assumptions of market efficiency could also be violated.