We use multivariate Generalized Autoregressive Conditional Heteroscedastic models to assess evidence of electricity market integration between Spain, Portugal, Austria, Germany, Switzerland and France from 7-1-2007 to 2-29-2012. Spillovers and price convergence are used as indicators of integration. Evidence of dynamic conditional correlation is found for the pairs Spain-Portugal, Germany-Austria and Switzerland-Austria. Weak evidence of integration is found between Spain-France and Germany-France since no cross volatility transmissions are estimated. There are increasing price convergence and significant mean and volatility spillovers in the rest of the country pairs. We conclude that the European Union target of achieving a single electricity market depends largely on increasing interconnections and efficient rules of market operation.