Both the regional health board and the local health centre have today issued alerts about high demand for their services.
According to the BBC, an internal critical incident has been declared by the Betsi Cadwaladr Health Board, which covers Llangollen.
The board described demand on its services over recent days as "unprecedented".
It said this was due to a combination of winter viruses, parents seeking help due to concerns about strep A and injuries related to the cold weather.
This has meant extremely long waits for patients to be seen - particularly at A&E departments.
"A lack of available beds in our hospitals is currently leading to unprecedented ambulance delays across the health board and we are working closely with local authority colleagues to support medically fit patients to be discharged from hospital," it said in a statement.
"Similar pressures are being experienced in other health boards and English trusts.
"This morning, we have declared an internal critical incident, which means we are struggling to cope with the prolonged, significant demand on the health system in north Wales."
"We are experiencing massive demand for our services this morning.
"We are doing our very best to deal with this demand but we are having to prioritise your calls based on clinical need to ensure that our poorliest patients can access our services when they need to."
"Many common winter illnesses can be managed at home. Please use the symptom checker at https://111.wales.nhs.uk/ to see whether you need to contact us or whether your symptoms can be managed at home."
Meanwhile, Llangollen Health Centre said this morning on social media: "We are experiencing massive demand for our services this morning.
"We are doing our very best to deal with this demand but we are having to prioritise your calls based on clinical need to ensure that our poorliest patients can access our services when they need to.
"Many common winter illnesses can be managed at home. Please use the symptom checker at https://111.wales.nhs.uk/ to see whether you need to contact us or whether your symptoms can be managed at home.
"NHS 111 Wales and Public Health Wales have a range of resources and advice to support parents and carers spot the signs of GAS infection including a new iGAS and Scarlet Fever symptoms checker tool. This tool can help parents decide when to treat their child at home and when it is appropriate to seek medical advice. https://111.wales.nhs.uk/encyclopaedia/s/article/streptococcusa(strepa)
"Thank you for your cooperation."