In an interview with 'Big Think' portal, Prof Hawking has said he's an "optimist" but the next few hundred years had to be negotiated carefully if the human race is to survive.
He said: "I see great danger for the human race. There have been a number of times in the past when survival has been a question of touch and go. The Cuban missile crisis in 1963 is one of these.
"The frequency of such occasions is likely to increase in the future. We shall need great care and judgment to negotiate them all successfully. But I am an optimist. If we can avoid disaster for the next two centuries our species should be safe as we spread into space."
Prof Hawking has warned that mankind was entering "an increasingly dangerous period of our history". "Our population and use of the finite resources of planet Earth and growing exponentially along with out technical ability to change the environment for good and ill.
"But our genetic code carries selfish and aggressive instincts that were a survival advantage in the past. It will be difficult enough to avoid disaster in the next 100 years let alone the next thousand or a million. Our only chance of long term survival is not to remain on Earth but to spread into space.
"We have made remarkable progress in the last 100 years but if we want to continue beyond the next 100 years our future is in space," the 'Daily Mail' quoted him as telling the portal.