Leeds Teaching Hospitals NHS Trust has warned of delays in its accident and emergency departments and asked people to consider alternatives to A&E.
The trust said only people with severe and life-threatening conditions should seek treatment at Leeds General Infirmary and St James’s University Hospital.
Suzanne Hinchliffe, the trust’s chief operating officer, said the situation had worsened after the Christmas period.
Prof Hinchliffe said: “Like all hospitals across the NHS, we have been experiencing very significant demand for our services, especially in our emergency departments. Now that the holidays are over, the situation has become even more serious.
“A&E at LGI and St James’s are extremely busy and I would like to ask people to find alternative care, except in the case of genuine emergencies.”
The trust said examples of conditions which should be treated in A&E included cardiac arrest, breathing problems, chest pains, stroke, severe burns and choking.
People with less serious conditions should seek help from their GP or pharmacist, or via the non-emergency helpline NHS 111.
They can also visit NHS walk-in centres and minor injury units. For a list of those facilities click here
Prof Hinchliffe added: “If you are not seriously ill, A&E may not be the best place for you to get the treatment you need and you may wait for a long time.
“Emergency medical staff are trained to deal with the most severe and life-threatening conditions.
“By seeking alternative care, you will be helping our highly trained urgent care staff to treat the patients only they can care for.”