Gavin Rossdale Steps Out Amid Gwen Stefani Divorce Filing

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Gavin Rossdale was carrying on with life as usual just before news broke that he and Gwen Stefani are divorcing after nearly 13 years of marriage.

The 49-year-old Bush frontman went shopping with his dog and a friend in Beverly Hills, California, on Monday, looking cool and casual as ever. Wearing shades, a plain white tee and sneakers, Gavin at least appeared to be pretty relaxed.

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WATCH: Gwen Stefani Files for Divorce From Gavin Rossdale

The British rocker and the 45-year-old No Doubt frontwoman announced their surprising split on Monday with a joint statement. "While the two of us have come to the mutual decision that we will no longer be partners in marriage, we remain partners in parenthood and are committed to jointly raising our three sons in a happy and healthy environment," the pair said.

But the cheating rumors are already beginning. According to TMZ, Gwen pulled the plug on her marriage because she believed he was cheating on her. However, the split was reportedly "a long time coming," as the two allegedly haven't been getting a long for a while now, and were both away from home a lot thanks to busy touring schedules.

But their time apart didn't seem to bother Gwen in February, when she told Cosmopolitan that both of them having their own individuality was key to their marriage. "It's good to have those days when we both do our own things," she said. "I think that's what keeps relationships going, when both people can be themselves and have their own individuality."

Gavin and Gwen actually met when Bush and No Doubt toured together in 1995, and married in 2002. Last November, the Voice coach admitted during an appearance on The Ellen DeGeneres Show that the two have definitely had their ups and downs in their nearly 20 years together.

"Like everybody else we go through our cycles of being so happy and then being like, 'Oh my gosh.' And then being so happy it's crazy," Gwen said of their marriage. "I mean I can't believe that I've known him as long as I have and we still have fun together."

In documents obtained by ET, Gwen cited "irreconcilable differences" in her divorce petition filed on Monday, asking for joint custody of the couple's three sons: 9-year-old Kingston, 6-year-old Zuma, and 1-year-old Apollo. Gavin filed his response at the same time, and is also asking for joint custody.

NEWS: 11 Times Gwen Stefani and Gavin Rossdale Got Real About Their Marriage and Kids

Gwen is certainly keeping busy these days, returning as a coach on the Voice this fall. ET caught up with her last month, when she was clearly excited about her team this season. "When you start to get to know them and get in the room with them and work with them, you really start to really understand what you got," she gushed. "The talent you got. It's super incredible." Watch below:

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