Bruce Willis's daughter Tallulah has shared intimate moments with her father amid his ongoing battle with frontotemporal dementia and aphasia

His 31-year-old fashion designer daughter is among his family members who have been caring for him, and has now posted snaps of her time with him, including one of her giving him a hug.

She captioned the image, posted to her Instagram Stories: "Sunday funday at Grams! Grateful (white dove emoji.)"

Tallulah's older sister Rumer, 36, also shared a heartfelt update in a Father's Day post, reflecting on the challenges her father now faces.

She wrote: "Today is hard, I feel a deep ache in my chest to talk to you and tell you everything I'm doing and what's going on in my life. To hug you and ask you about life and your stories and struggles and successes."

The House Bunny star made reference to Bruce's struggles with speech and memory, admitting, "I wish I asked you more questions while you could still tell me about it all."

She expressed gratitude for the moments she still shares with her father, adding: "I know you wouldn't want me to be sad today so I'll try to just be grateful reminding myself how lucky I am that you're my dad and that you're still with me and I can still hold you and hug you and kiss your cheek and rub your head I can tell you stories."

Rumer also posted a touching photograph of Bruce with her two-year-old daughter, Louetta, noting: "I can watch the way your eyes light up when you see Louetta I will be grateful for every moment I have with you. I love you so much dad happy Father's Day."

Emma Heming paid tribute to her husband on Instagram, writing: "Happy Father's Day to all the dads living with disability or disease, showing up in the ways they can and to the children who show up for them."