We investigate return spillover effects and depict a connectedness network among U.S. and Asian stock markets, comparing the spillovers during three crisis sub-periods and the entire period. Our findings are summarized as follows: First, regarding a puzzle in Choi (Econ Anal Policy 73:179-193, 2022) we find that total and net-pairwise spillover index during the global financial crisis (GFC) period are greater than those during COVID-19 pandemic period for stock markets studied, with the exception of Hong Kong which shows contrary results. Second, particularly, we decompose total spillover into two directional spillovers. The directional spillover from U.S. to Asian markets is greater during GFC period than that during COVID-19 period, whereas the directional spillover from Asian markets to U.S. display the contrary results. Third, different from S&P500 used by the literature, we use DJIA index to obtain the results conformable with the studies showing that U.S. is the strongest contributor and net transmitter of shocks to 9 Asian markets. Finally, analogous to findings in the literature, spillover indices across stock markets intensify during crisis periods. Our findings provide practical implications that understanding spillover effects among U.S. and Asian markets can help investors and portfolio managers to execute diversification strategy.