Motivated by financial liberalisation investors seek for new investment opportunities through international portfolio diversification. To this end we explore any asymmetric causal relationship between developed European stock markets (Germany, France and UK) and emerging Baltic markets, namely Estonia, Latvia and Lithuania. Our analysis focuses on the period before and after the countries' EU accession and pre- and post the global financial crisis. For this purpose, both the standard parametric test for causality and a novel nonparametric test for causality-in-quantiles are employed. The results of both the parametric and nonparametric Granger causality test support a causal relationship in mean that runs from all of the major markets to the Baltic markets across both samples. The results imply the existence of significant nonlinear return and volatility spillovers from European markets to Baltic markets. Policy implications for international investors are also discussed.