Neither Crowe nor his musician wife, Danielle Spencer, was available for immediate comment and their Twitter accounts gave no hint of any split.
But Don Spencer, Spencer's father, confirmed the couple had separated and said their main priority was the children, Australian TV station Ten Network reported.
New Zealand-born Crowe was filming the Biblical epic "Noah" in the United States, while Spencer remained in Sydney with their two sons, the Sydney Morning Herald said.
The couple married in 2003 and were seen as a solid partnership in showbiz circles. Spencer was believed to have tamed Crowe's temper while pursuing her own music career.
"All that stuff has nothing to do with me as a person," Spencer had said of her husband's fame, according to the newspaper.
Crowe won the best actor Oscar for the 2000 movie "Gladiator" and was nominated for the same award for the "The Insider" (1999) and "A Beautiful Mind" (2001).
(Reporting by Maggie Lu Yueyang; Editing by Elaine Lies)
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