This paper models volatility spillovers from mature to emerging stock markets, tests for changes in the transmission mechanism during turbulences in mature markets, and examines the implications for conditional correlations between mature and emerging market returns. Tri-variate GARCH-BEKK models of return in mature, regional emerging, and local emerging markets are estimated for 41 emerging market economies (EMEs). Wald tests suggest that mature market volatility affects conditional variances in many emerging markets. Moreover, spillover parameters change during turbulent episodes. In the majority of the sample EMEs, conditional correlations between local and mature markets increase during these episodes. While conditional variances in local markets rise as well, volatility in mature markets rises more, and this shift is the main factor behind this increase in conditional correlations. With few exceptions, conditional beta coefficients between mature and emerging markets tend to be unchanged or lower during turbulences.