Mr Cable, the party’s treasury spokesman, predicted the SNP administration could find itself on a "collision course" with a Government led by David Cameron that had no Scottish mandate.
Such a scenario was likely within two years, and unless action was taken it could lead to conflict and even Scottish secession, he added.
Mr Cable said this was because the Tories, while possibly having "one or two" Scottish MPs, would have no support north of the border. He said the scenario would be a "terrible tragedy" for Britain because the UK was "one of the great creations of this country".
Speaking at a fringe event at his party’s conference in Bournemouth, Mr Cable said the Liberal Democrats with their federalist policies of greater devolution could prevent the crisis.
He highlighted the "unfinished consequences of Britain's devolutionary settlement.” Mr Cable added: "I think that within a year's time, maybe two years' time, there will be a major constitutional crisis in Britain.
"This Government has devolved substantial powers to Scotland, rightly, absolutely rightly...and that has happened.
"But there is a scenario looming up, which we hope will not happen, but we may get a Conservative Government, certainly polls suggest that might happen with probably one or two Scottish MPs quite likely, but absolutely no mandate whatever north of the border.
"You have a nationalist government in Edinburgh on collision course with a Government in London that is not interested, actually would probably quite like to get rid of all those Labour MPs north of the border, and the whole future of the UK will come into question.
"I believe that would be a terrible tragedy because the United Kingdom is one of the great creations of this country - Britain, and something we should be proud of.
"The only party which has got practical suggestions about how to make this arrangement work is ours because we are committed to genuinely federal solutions - letting the Scots and for that matter the Welsh and the Northern Irish, have much more genuine revenue-raising powers, have genuine devolution...within the UK.
"Unless we grasp this, the situation is allowed to drift, it's going to lead to conflict and possibly secession. That is probably the most important constitutional issue we are going to face."
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