Bruce Willis' daughters Scout and Tallulah are "so proud" of Emma Heming Willis for speaking about their father's health battle.

The 68-year-old 'Die Hard' actor has Frontotemporal dementia (FTR), which is an uncommon form of the disease which causes a deterioration in personality, behaviour and language.

Emma spoke about her struggles dealing with the "grief and the sadness" of her husband's decline in health during an emotional interview this week on 'Today'.

Now, Scout and Tallulah - who are Bruce's children from his marriage to Demi Moore - have heaped praise on her for speaking out.

Scout, 32, wrote on Instagram: "I truly could not be more proud of @emmahemingwillis for being willing to step out into the public eye, (even thought it's terrifying!!!) to share our family's story in service of spreading awareness about FTD.

"Emma you are such a champion for this cause and you inspire me EVERY SINGLE F****** DAY with your bravery and deep loving.

"Your courage is moving mountains #ftd #ftdawareness. (sic)2

And Tallulah, 29, added: "So proud of my family. @emmahemingwillis"

Bruce also has daughter Rumer, 35, with Demi - to whom he was married from 1987 to 2000 - while he and Emma have Mabel Ray Willis, 11, and Evelyn Penn Willis, nine, together.

During the interview, Emma admitted she has learned that "dementia is hard" on everyone involved.

She said: "It’s hard on the person diagnosed, it’s also hard on the family. And that is no different for Bruce, or myself, or our girls.

"When they say this is a family disease, it really is."

She admitted coming to terms with Bruce's condition has been "the blessing and the curse" but she's thankful he was able to get a definitive diagnosis.

She added: "To finally understand what was happening so that I could be into the acceptance of what is — it doesn't make it any less painful, but ... just being in the know of what is happening to Bruce makes it a little easier."