Kate Hudson is due ANY MINUTE!

The actress, a full nine-months pregnant with her baby girl with boyfriend Danny Fujikawa -- in fact sources close to the actress have said she's past her due date.

We spotted Kate and Danny out in Pacific Palisades village, near their home, on Sunday. The couple grabbed an Acai Bowl from Juice Crafters and window shopped.

Danny stayed true to his usual funky style with some brightly-colored tropical-print cropped pants, while Kate wore a billowy black dress to hide her bursting baby bump! The two definitely didn't appear to be dying to have their picture taken, but Kate laughed as she hid behind her man ...