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Friends and family of the 62-year-old Bee Gees star have been keeping a bedside vigil since he slipped into a coma last week, with older brother Barry even trying to rouse him with singing.
Now finally Robin - who had just achieved remission from colon and liver cancer - is believed to be showing small signs of recovery.
A source told The Sun newspaper: "There were flickers of life from Robin. His eyes moved and there was an attempt at speech.
"It was a good sign he is fighting hard for his life but he is certainly not out of the woods yet. The family have to remain very cautious."
'Karmic price'
His health battle started 18-months ago when he was diagnosed with cancer after being rushed to hospital with abdominal pain.
The teetotal vegan subsequently underwent seven rounds of chemotherapy, and previously admitted he wonders if his family tragedies - including the deaths of his brothers Andy in 1988 and Maurice in 2003 - are a "karmic price" for the band's worldwide success.
He said: "I sometimes wonder if all the tragedies my family has suffered, like Andy and Maurice dying so young and everything that's happened to me recently, is a kind of karmic price we are paying for all the fame and fortune we've had.
"But we've worked hard for everything we've achieved."
