The casualty departments at Royal Lancaster Infirmary and Furness General Hospital are so busy, patients have been urged to go elsewhere if they can.
In a statement, the trust that runs the two hospitals said its emergency departments were 'very busy today', and said it was asking people 'for their help by considering using other healthcare services rather than A&E'.
The University Hospitals of Morecambe Bay NHS Foundation Trust said: "We do occasionally experience sudden increases in attendance, which can impact on the time for patients to be seen, treated and either discharged or admitted.
"At the moment, patients are likely to experience long waiting times, whilst those who need urgent treatment are seen first.
"We are asking the public to help them to make sure staff are free to treat those most in need, such as those who have a serious illness or injury. If they do attend, we would ask that they please be patient with staff who are doing their best in difficult circumstances.
"Whilst we will see and treat all patients who attend, there are those who could be better treated elsewhere. We know it can be difficult when someone is unwell so if you aren’t sure whether or not to attend the A&E, please ring the NHS advice line on 111 who are trained to help.
"If you have a minor illness or injury that needs attention, you can visit your nearest pharmacist, Primary Care Assessment Centre, or speak to your GP.
"An emergency is a serious or life-threatening injury and condition, such as a suspected heart attack, acute confused state and fits that are not stopping, loss of consciousness, breathing difficulties, chest pain, head injuries or severe bleeding that cannot be stopped. If someone is seriously ill or injured and their life is at risk, then 999 should be called."