In this paper we use the univariate and multivariate GARCH models to investigate the volatility behavior of four Mediterranean stock markets (Morocco, Turkey, Spain, and France) over the period 2000-2020. Our results show strong evidence of persisting of volatility in each of these markets. We also find that both the univariate and the multivariate approachs capture well the arch and garch effects. We analyze the conditional covariances, and co-volatility spillovers between the Moroccan stock market and the three other medeteranien stock markets. The empirical analysis will be based on the diagonal BEKK model, from which the conditional covariances will be used for studying co-volatility spillovers.