Patients who are due to have operations over the next few days are being warned they may be cancelled.
It's because of a lack of surgical beds in Noble's Hospital - that's due to the closure of two wards.
Norovirus has been confirmed on Ward 8 and there's a suspected outbreak of viral gastroenteritis on Ward 5.
The Department of Health and Social Care says it's putting 'significant pressure' on the remaining number of beds available within the hospital.
Members of the public are being urged not to visit unless absolutely necessary - anyone who's had the illnesses themselves is asked to wait three days before visiting.