Durham County Council’s statutory licensing sub-committee is to discuss the licences after concerns were raised by the police.
The committee will review the shops’ licences at County Hall, in Durham, on Friday, June 6, to decide if they should be revoked.
The Premier Convenience Store, on Main Street, was targeted by police on Saturday, September 21 last year as part of Operation Hampden.
Shop staff breached the law to sell a 16-year-old teenage girl a bottle of Pinot Grigio wine.
Then staff repeated the mistake when a second teenager bought a bottle of Chardonnay wine on Friday, February 21 as part of Operation Xavier.
The shop has a licence to sell alcohol to adults between 8am and 11pm Monday to Saturday and from 10am to 10.30pm on Sunday.
The Jubilee Fields Convenience Store, on Coronation Avenue, Shildon, also twice sold alcohol to a 16-year-old girl on Saturday, September 21, last year.
A 16-year-old girl also caught out staff as she bought a bottle of white wine on Friday, February 21 from the store.
The shop can serve alcohol to adults between 8am and 11pm Monday to Saturday and from 10am to 10.30pm on Sunday.
Talks have taken place between groups like Durham County Council and the shop’s owners to try to install measures to avoid a repeat.