Real Madrid's Gonzalo Higuain (bottom) celebrates with team-mate Alvaro Arbeloa after scoring his second goal against Ajax during their Champions League Group G soccer match at the Santiago Bernabeu stadium in Madrid, September 15, 2010.[Xinhua/Reuters Photo]

AC Milan and Real Madrid kicked off their Champions League campaigns with 2-0 victories on Wednesday night as English rivals Chelsea and Arsenal opened with high-scoring wins.

Zlatan Ibrahimovic scored a brace on his Champions League debut for AC Milan in a victory over visiting Auxerre, and new Real Madrid coach Jose Mourinho presided as the nine-time champions beat Ajax thanks to efforts from Xavi Alonso and Gonzalo Higuain.

After Milan struggled to score in the first half, Ibrahimovic broke the deadlock in the 66th after linking up with Kevin Prince Boateng and Ronaldinho.

His second came just three minutes later, and completed a slick counter-attacking move that began with Robinho carrying the ball from the defense and culminated in Ibrahimovic sweeping home Ronaldinho's deft pass.

Before then, Auxerre had the better of the chances. Valter Birsa and Steeven Langil had early shots and Adama Coulibaly headed against the bar.