In this study to analyze the asymmetric volatility spillovers. We study in the stock and bond markets in Borsa Istanbul. The research covers 2003-2019. Financial crises have increased the importance of the transition between the stock and bond market. Apart from the full period, the 2008 financial crisis period examines separately in order to see the effects of the spillovers during the crisis period. First, asymmetric volatility tests with the sign bias test. Then, whether the stock and bond market volatility is asymmetric, investigate with the GJR-GARCH model. Finally, asymmetric volatility between the two markets test with the VARMA-AGARCH model. According to the asymmetric volatility test results, negative volatility asymmetry exists in the bond market in full period. Asymmetric volatility is positive in both market in the crisis time. Return spillovers from the stock market to bond market in full period. It is opposite direction during the crisis period. We have found volatility spillovers bidirectional among the stock market and the bond market. However, during the global crisis period, volatility spillover is bidirectional from the stock market to the bond market.