Weather officials have put in place 11 flood alerts which could affect residents in several regions across the country.
Residents are being warned to prepare for the possibility of flooding in areas covered by the alerts.
Storm Dudley is expected to hit northern parts of the UK on Wednesday and Thursday before Storm Eunice arrives on Friday.
Amber and yellow wind warnings are in place for northern England, Scotland and Northern Ireland from 3pm on Wednesday until 9am on Thursday.
A yellow warning will also cover the southern part of Scotland, northern England and Northern Ireland on Friday until 9pm.
Met Office meteorologist Tom Morgan, said: “This whole week is going to see quite a disturbed weather pattern developing across the UK”.
He said western parts of Scotland will “bear the brunt” of the strongest winds which could cause “widespread disruption.”