The 62-year-old singer's family have been keeping vigil at his bedside at a hospital in Chelsea, west London.
They are understood to include his wife, Dwina, brother Barry, 65, daughter Melissa, 37, and sons Spencer, 39, and Robin-John, 29.
Gibb had surgery on his bowel 18 months ago for an unrelated condition, but a tumour was discovered and he was diagnosed with cancer of the colon and, later, of the liver.
It had been thought his cancer was in remission as early as last month, but the latest deterioration in his health coincides with reports of a secondary tumour.
A statement on the singer's website RobinGibb.com said: "Sadly the reports are true that Robin has contracted pneumonia and is in a coma. We are all hoping and praying that he will pull through."
Gibb's twin brother and bandmate, Maurice, died from the same bowel condition that initially led doctors to operate on Robin.
His younger brother Andy, who was not part of the Bee Gees but a successful singer in his own right, died in 1988 from heart failure at 30.
Robin Gibb has enjoyed a musical career spanning six decades, from humble beginnings as part of a sibling trio in 1950s Manchester to his most recent classical venture, a requiem for the Titanic.
In the interim, he sang some of the 1960s and 1970s greatest hits, including Massachusetts, I've Gotta Get a Message to You, Lonely Days, How Can You Mend a Broken Heart, How Deep is Your Love and Stayin' Alive. The Bee Gees are best remembered for their contribution to the soundtrack of the 1977 film Saturday Night Fever.
Gibb last performed on stage in February, supporting injured servicemen and women at the Coming Home charity concert held at the London Palladium.
He had been due to premiere his classical work, The Titanic Requiem, this month with son Robin-John, but the event went ahead without him because of his poor health.
