Medical experts are advising people to only go to A&E in an emergency.
The request was issued as Accident and Emergency departments at Calderdale Royal Hospital and Huddersfield Royal Infirmary are reported as extremely busy.
Dr Mark Davies, Clinical lead for Emergency Care and Calderdale and Huddersfield NHS Foundation Trust, said: “There are currently long waits in both our emergency departments.
“The numbers of people presenting with non-emergencies is contributing to the situation. We would ask them to consider other alternatives than coming into A&E.
“Emergencies will always receive priority in our departments and we would ask everyone else to bear with us and expect to wait.”
People attending with long-standing ailments which aren’t medical emergencies, are a factor in the delays explained a Trust spokesman.
A&E departments are for life-threatening emergencies, such as: loss of consciousness, acute confused state and fits that are not stopping, persistent, severe chest pain, breathing difficulties, severe bleeding that cannot be stopped, severe allergic reactions, severe burns or scalds
The spokesman added that many people are also visiting A&E at Calderdale Royal hospital with the norovirus, also known as the winter vomiting bug, which is affecting waiting times.
Dr Alan Brook, Chair of NHS Calderdale CCG said: “The norovirus is passed to others very easily, so If you have diarrhoea or are vomiting or feeling nauseous, please avoid going to busy places, such as work, school or hospital for at least 48 hours after the symptoms have passed.”
Speak to a pharmacist, GP or call NHS 111 in the first instance.