Stallone who has daughters Scarlet, 20, Sistine, 24, and Sophia, 25, with his wife, said: “I love my family. We are amicably and privately addressing these personal issues.”
The couple celebrated their silver wedding anniversary earlier this year.
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The Hollywood star – who also has Seargeoh, 43, with actress Sasha Czack, as well as another son, Sage, who died in 2012 – took to social media at the time to celebrate the landmark.
Alongside some throwback photos of them together, Stallone wrote on Instagram: “Happy 25th anniversary to my amazing wife. There is not enough words to describe what this incredibly selfless dedicated, patient, woman has meant to our lives and I only wish they could be another 25! Thank you sweetheart! (sic)”
Flavin also celebrated their silver wedding anniversary on social media.
Alongside her collection of photos, she said: “Happy 25th wedding anniversary to us! (heart emojis) Thank you for always keeping me laughing, loving and protecting our beautiful family! (sic)”
The model also said their marriage was “getting better every year”.
She wrote on Instagram: “Our marriage keeps getting better every year! I can’t wait to spend the rest of our lives together! (heart emojis) (sic)”
However, the heartfelt post was removed shortly before it emerged that the couple – who first met at a restaurant in Beverly Hills, California, in 1988 – are heading for a divorce after 25 years of marriage.