A spokesperson from Buckinghamshire Healthcare Trust said: "Currently, the A&E at Stoke Mandeville Hospital is particularly under extreme pressure.
"Staff are working exceptionally hard across all services to make sure people receive the care and treatment they need.
"Unless there is an emergency, we urge people to seek advice and treatment at other centres including local pharmacies, GP surgeries and the Urgent Treatment Centre in High Wycombe."
They are advising that non-urgent patients at Stoke Mandeville A&E can expect long waits, and urge people to use hospital accident & emergency departments for emergencies only.
If it is not an emergency and you are unsure what to do contact NHS 111.
Trained staff will advise and guide you to the right service - including booking an out of hours GP appointment. The NHS 111 service is open 24 hours a day, every day and also available online https://111.nhs.uk/Ambulance services should be called via 999 for any life threatening situation.
The Spokesperson added: "We apologise to anyone who has had to wait a long time to be seen, but staff must prioritise the most urgent cases first."