Maurice's mother and twin brother Robin flew from the UK to be at the hospital, and the family released a statement saying: "His love and enthusiasm and energy for life remain an inspiration to all of us. We will all deeply miss him."
The Bee Gees were massive during the 70s
Gibb was in the Bee Gees with Robin and elder brother Barry, and together they were one of biggest bands of 70s, although they were also very successful before and after that decade.
Maurice was the member of the trio that sang the really high parts of the group's songs, and came up with a lot of important instrumental parts on their records.
Maurice (right) with brothers Barry and Robin
They are most well known for the songs they wrote for the film Saturday Night Fever, including the huge track Stayin' Alive, which helped take disco music from underground nightclubs into the mainstream.
The Bee Gees are also among the top five of the highest selling recording artists of all time, with The Beatles, Elvis Presley, Michael Jackson and Paul McCartney as a solo artist.
Because the songs they wrote are so good, lots of other bands have made cover versions of them, including Elvis, Destiny's Child and their song Sacred Trust is in the top 10 at the moment, recorded by One True Voice.