The two storms are set to hit one after the other, as Storm Dudley today brings a yellow warning for strong winds at 1pm across central Scotland and northern England, with a more severe amber warning for wind landing at 2pm.
However, with both warnings expiring by early tomorrow morning, Storm Eunice will bring a third warning - a yellow alert for wind and heavy snow which has been issued between 3am and 6pm on Friday.
Scotland is now set to face three days of widespread disruption.
The Met Office says that Storm Dudley lands on Wednesday afternoon, coming in from the west.
It said: “Very strong westerly winds are expected to develop across southwest Scotland and northern parts of Northern Ireland on Wednesday afternoon, extending eastward across southern Scotland and northern England during the evening.
"There is still some uncertainty in the timing and location of the strongest winds but inland gusts of 60-70 mph are likely, perhaps briefly 75-80 mph in a few places, mostly exposed sites.”
The Met Office says of Friday’s warning: “Snow, heavy in places, is likely to develop on the northern side of Storm Eunice as it moves across the UK on Friday.
"There is still uncertainty in the track of Storm Eunice and not all areas within the warning area are expected to see snow.
"However, some places may see around 5 cm of snow at low levels away from coasts.
"Accumulations are expected to be significantly higher over hills though with 10-20 cm perhaps up to 30 cm possible above around 250 metres.
"Strong winds occurring at the same time may lead to very poor visibility, blizzard conditions and drifting of lying snow.”
Katharine Smith, Environment Agency Flood Duty Manager, said: “Please remember to take extreme care on coastal paths and promenades.
"We urge people to stay safe on the coast and warn wave watchers against the unnecessary danger of taking ‘storm selfies’.
"Flooding of low-lying coastal roads is also possible and people should avoid driving through flood water as just 30cm of flowing water is enough to move your car."