Two homes, a garage, a shed and a pub were targeted sometime between Saturday, 20 July and Sunday, 21 July 2019.
Homes on Marsh Lane, New Mills, and on Hockerley New Road, Whaley Bridge, a garage on Miller’s Vale, New Mills, a shed on Park Terrace, Glossop, and the Old Bulls Head Pub, on New Road in Buxworth were burgled.
A mobile phone, a mountain bike and a laptop and a set of car keys were among the items stolen.
None of these incidents took place during the recent evacuations related to the risk of the Toddbrook Reservoir breaching.
Police ask: "Do you recognise these men or do you have any information about the incidents which may help with our enquiries?
"If so, please get in touch using one of the following non-emergency contact methods.
"Please quote the reference number 19*381126 and name of the officer in the case, DC Tim Brown, in any correspondence."