This study tests the hypothesis that the ongoing restructuring process in the European electricity sector, as well as market participants' adaptation to the new legal framework, have caused electricity wholesale day-ahead prices to converge towards arbitrage freeness. Using hourly cross-border capacity auction results at the Dutch-German and at the Danish-German border for the years 2002 to 2004, and the respective spot prices. We estimate a time-varying coefficient model based on the law of one price (LOP). The results of these estimations are used to calculate the speed of convergence towards the LOP. While the German-Dutch prices and the German-West Danish prices are clearly developing towards arbitrage freeness, the German and East Danish prices do not exhibit significant convergence.