The first one's from 10pm Wednesday 6th February.
The first warning expires in 9am Thursday morning.
The second is from midday on Friday until 6pm on Saturday.
Winds are expected to reach up to 70 miles per hour along the coast.
The Met Office website says:
A period of very strong and gusty winds is likely on Wednesday night and Thursday morning. Strongest winds will be across South West England and South and West Wales late evening, with gusts of 60 to 70 mph on coasts and 50 to 60 mph inland. Elsewhere winds will be strongest after midnight, with gusts of 60 mph on coasts and 50 mph inland before easing during Thursday morning.