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Medway hospital is asking people to think before they go to A&E as they are struggling to cope with "extremely high" numbers of patients.
People with minor illnesses are facing very long waits at the emergency department and a senior matron says they do not have enough beds.
Health bosses have asked people to consider going to other services for treatment.
A spokesman said: "The Emergency Department at Medway Maritime Hospital is currently experiencing extremely high numbers of attendances. Many of these patients could have received the treatment they needed more quickly from other local services."
Senior matron Clare Hughes said: “Patients inappropriately visiting the Emergency Department are placing considerable strain on the hospital.
"We’re now in the very worrying position of having more people coming in than we have beds available. This can have very serious consequences for seriously ill patients who need our help.
“We have to treat the most unwell patients first, which means that those coming to the Emergency Department who have minor illnesses or non-life-threatening conditions are experiencing very long delays.
"Please consider whether our Emergency Department is the right option for you before coming."
If you have a minor illnesses or a non-life threatening condition, the advice from the trust is to:
A spokesman added: "We urge you to consider these other options, where you are likely to receive the treatment you need more quickly before visiting the Emergency Department.
"This will reduce the pressure on the department and also means we can provide attention to the people who really need our care."