The closure of the Dumfries and Workington HMV stores will result in the loss of 16 jobs-eight jobs from each of the two stores.
"As part of our ongoing review of HMV's financial position, we have now completed a review of the store portfolio and have identified 66 loss making stores for closure.
"This step has been taken in order to enhance the prospects of securing the business future as a going concern.
"We continue to receive strong support from staff and are extremely grateful to them for their commitment during an understandably difficult period.
"All other key stakeholders remain very supportive and I continue to be hopeful of securing a future for the restructured business."