This paper investigates volatility transmission patterns between the US and Eurozone stock markets differentiating between low and high volatility periods which tend to be related with international crisis. Our approach let us distinguish the spillover intensities between markets in calm and crisis periods and also tests for a potential increase of market comovements during these last periods. State-Dependent Volatility Impulse-Response Functions (SD-VIRF) are also introduced considering different responses of stock markets during detected periods of high and low volatilities. The results show that volatility spillovers intensities increase during turmoil periods and it is also find an increase of conditional correlation during times of market jitters.