The former Fraser star discussed his marriage to new wife Kayte Walsh in a discussion with Oprah Winfrey, but refused to mention Real Housewives star Camille's name.
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Grammer opted to refer to his ex-wife using expressions such as "that person" for the duration of the candid interview.
The actor revealed that he "lacked the courage" to end his 13-year relationship with Camille, and acknowledged her involvement with his success.
"I did believe that I owed something to that person, that I owed [her my] fame," he explained.
When asked by Winfrey whether he would say her name, Grammer simply answered: "No."
Grammer, who currently stars in Boss, recently remarried Walsh in a Las Vegas ceremony.
His interview on Oprah's Next Chapter will air this Sunday (August 26) on OWN.
