Trading at the 5,000sq ft and 6,000sq ft former Somerfield stores in Keynsham and Minehead had been "disappointing" with a "negative effect on profitability and sustainability", AWG managing director John Pattison said.
However, fears over the impact of new supermarket developments close to the stores had brought forward the decision to cease trading.
"In Minehead, the impending arrival of a new Morrisons store in the town has led us to make a commercial decision to close the Eurospar in The Avenue. In Keynsham, we similarly face the impending threat of new competition in that Tesco will open in the town, very close to our store, and we have therefore had to make a similar decision," Pattison added.
The group now plans to place much greater focus and support behind the four independent Spar stores in the Minehead area, which are all located within a mile of each other, and the last remaining company owned Eurospar store in Liskeard.
This would enable the group to be "best positioned to defend against the new competition," Pattison added.
Trade at the 8,000sq ft Liskeard store has been more successful, and the store is earmarked for further development with plans for a minor refit of the outlet in October.
The Minehead store will close on September 25, and the Keynsham store on October 9.