The first incident took place at about 3.50am at a premises on the High Street in Haddington, when entry was forced and a low three-figure sum of cash was stolen.
Another property in Musselburgh's High Street was broken into at about 4.25am, although nothing was stolen.
Officers are treating these incidents as linked and are urging anyone who saw suspicious behaviour in the areas, or who may have information which can help, to get in touch.
The first suspect is described as wearing a khaki-coloured hoodie and black trousers, with the second suspect wearing a black hoodie and dark trousers.
They are believed to have been travelling in a yellow or orange-coloured Ford Focus.
Detective Sergeant Jordan Sharp of CID said: "Although only a small amount of money was stolen, these incidents have caused disruption to the businesses and we're asking for the public's help as part of our ongoing enquiries.
"In particular, anyone who may have captured the car or the suspects on private CCTV, or even on dashcam footage, is urged to contact us as soon as possible."
Anyone with information should contact police on 101, quoting reference number 0461 of 29th August for Haddington and 0349 of 29th August for Musselburgh.
Alternatively, contact Crimestoppers anonymously on 0800 555 111.