[en]This paper introduces a kernel-based nonparametric inferential procedure to test for Granger-causality in distribution. This test is a multivariate extension of the kernel-based Granger-causality test in tail-event introduced by Hong et al. (2009) and hence shares its main advantage, by checking a large number of lags with higher order lags discounted. Besides, our test is highly exible as it can be used to check for Granger-causality in specific regions on the distribution supports, like the center or the tails. We prove that it converges asymptotically to a standard Gaussian distribution under the null hypothesis and thus it is free of parameter estimation uncertainty. Monte Carlo simulations illustrate the excellent small sample size and power properties of the test. This new test is applied for a set of European stock markets in order to analyse the spill-overs during the recent European crisis and to distinguish contagion from interdependence effect.[/en]