perhaps check and see if these people married in Hexham,
I’ve had a quick look and I don’t believe these marriages took place in Hexham. These are licences issued by the Diocese of Durham where one of the parties happened to live in Hexham (hence the listing in the ‘places’ index). The marriages would have taken place elsewhere, somewhere in the Diocese of Durham.
The Durham bonds 1590-1837 have already been transcribed on Durham Records Online.
At this time Hexham and Hexhamshire were a ‘peculiar’ of the Diocese of
York and Licenses to marry there would have been issued by that Diocese or by its representative in Hexham - the situation was complex to say the least! For instance, Peter Burrell,who issued some of the licenses which have been quoted here, was an official of the Diocese of Durham, but he also acted as a representative of the Archbishop of York in Hexham.
What Andy is searching for are the Licences which were issued for marriages which actually took place in Hexham, and these don’t appear to be online.
