Gwen Stefani & Gavin Rossdale Divorce -- She Believes He Cheated

Gwen Stefani pulled the plug on her 13-year marriage to Gavin Rossdale because she believed he was cheating on her.

We're told Gwen and Gavin have not gotten along for some time. As one source put it, the split was "a long time coming."

We're told Gwen complained about Gavin being away from home too much, touring with his band Bush from December 2014 through March 2015. One source says Gwen put pressure on him to stop touring and stay home. For his part, he felt it she was hypocritical because she was on the road too.

Our sources say Gavin is a very good father, so both sides are seeking a joint custody arrangement.

As TMZ first reported ... Gwen filed for divorce Monday.