The Met Office has issued amber “be prepared” alerts for wind covering Scotland for Monday overnight into Tuesday.
Warnings for wind at the lesser yellow “be aware” level were also put in place for Northern Ireland, Wales and the north of England for Monday morning.
It comes just as the country sees off Storm Gertrude, which brought gusts of more than 100mph in places as well as heavy rain and snow.
Gusts of 70-80mph are now expected widely, while 90mph is possible in the most exposed areas, especially across the Western Isles and along the west coast.
The latest warnings include some yellow ones for rain for northern and central areas of Scotland.
The Met Office’s chief forecaster’s assessment said: “An area of low pressure is moving east across the Atlantic, deepening as it does so, before arriving across the north-west of the UK on Monday.
“Gale to severe gale-force, west to south-westerly winds are expected to develop on the southern and western flanks of this system, firstly affecting western Scotland from late afternoon before progressing east through the evening and overnight. Storm-force winds are likely in the most exposed areas.
“Winds should ease early on Tuesday morning as the system clears away to the north-east.”
It also warned of some large waves which could lead to flooding on coastal roads.
Scotland’s transport minister Derek Mackay said there was “every likelihood” for travel disruption over the coming days.
“The wintry weather is forecast to deteriorate tomorrow with the arrival of Storm Henry which carries an amber alert for high winds from Monday afternoon, continuing through the peak on Tuesday morning,“ he said.
On Saturday, routes in Tayside were affected by snow, with a number of collisions reported during the morning, particularly on the A90.
Motorists were also advised to avoid the A9 at Drumochter Pass, Dalwhinnie, because of the heavy snow.
On the A82, the snow gates were closed at Tyndrum, Bridge of Orchy and Glencoe.
The gates were also closed on the A93 from Braemar to Glenshee, the A939 from Tomintoul to Cock Bridge, and the A821 Duke’s Pass.
Caledonian MacBrayne is advising ferry passengers to check ahead for disruptions across the network.
Ross Moran, operations general manager, said: “Storm Henry is set to present significant operational challenges.
“As with any adverse weather, we would ask passengers to consider whether their journey is absolutely necessary and to regularly check for route disruptions across the network.
“Our website, Twitter and app all provide continuously updated travel information - our customer services team keeps these channels absolutely current and they all provide the best and latest details of our operations.
“We are committed to working as hard as possible to deliver optimal service cover, but with such adverse conditions predicted, widespread disruption is likely.”