The Hambleton, Richmondshire and Whitby Clinical Commissioning Group is proposing to transfer some paediatric and special baby care to the James Cook University Hospital in Middlesbrough, after senior doctors raised concerns over safety.
As paediatricians at the Friarage retire, there are fears the hospital will struggle to meet national standards. The move would also affect maternity services.
The proposals have angered people served by the hospital, which covers rural parts of North Yorkshire. Last month, several thousand took part in a march to demonstrate. Many are concerned about having to travel the extra 25 miles to Teesside.
Doctors are looking at several options for the future and want people to attend the last in a series of public meetings at Bedale Hall this evening.