Jennifer Lopez, Marc Anthony say they are breaking up

The superstar couple, in a joint statement to People magazine, said, "We have decided to end our marriage. This was a very difficult decision. We have come to an amicable conclusion on all matters."

"It is a painful time for all involved and we appreciate the respect of our privacy at this time."

Lopez, 41, and Anthony, 42, were married in a June 2004 ceremony and they have 3-year-old twins, Max and Emme.

It is Lopez`s third marriage, Anthony`s second.