Kate and Oliver Hudson were "not surprised" their father Bill disowned them.
The musician publicly said his two children were "dead" to him over the weekend, but the 'How To Lose a Guy in 10 Days' actress and her 'Scream Queens' star brother were not shocked by his comments as they have been well aware of his feelings towards them "forever".
A source close to the siblings said the pair have had "zero relationship" with their father for several years.
The insider added to Us Weekly magazine: "They don't care and are not surprised by this.
"It's been this way, and he's been saying this stuff, forever."
Meanwhile, another source suggested the 65-year-old singer - who was married to Kate and Oliver's mother, Goldie Hawn, from 1976 to 1982 - controversially shunned his children in an attempt to "clear his name".
The insider said: "They weren't surprised at all that Bill spoke out.
"He's always trying to clear his name and his image."
The public breakdown of the film stars' relationship with their father began earlier in June when Oliver wished his sister a "Happy abandonment day" online on Father's Day, spurring Bill's comments on Sunday (28.06.15).
Bill said: "I say to them now, 'I set you free'. I had five birth children but I now consider myself a father of three. I no longer recognise Oliver and Kate as my own.
"I would ask them to stop using the Hudson name. They are no longer a part of my life. Oliver's Instagram post was a malicious, vicious, premeditated attack. He is dead to me now. As is Kate. I am mourning their loss even though they are still walking this earth."