NSK is right to say that the stamps of Donetsk and Luhansk could be only used for local mail (not to Russia even).
Mail to / from Russia had to be sent via special sorting centres in Russia (Post Boxes) wherefrom it was further delivered from / to the rebel territories.
When sent from there, mail was paid for at their "international" post rates, no stamps were affixed (and no name of the "republics" could be mentioned on the cover, either). Stamps were only affixed at those Post Boxes.
Unlike
NSK, I would not call them bogus stamps (I believe you meant they were not recognized by the UPU

- what would you say then about stamps from Northern Cyprus and the Republic of China (Taiwan)?).
Those stamps were widely used within the "republic's on commercial mail, even wider than anywhere else due to so specific features of their documentary circulation legislation.
Since their "unification" with Russia, Russian stamps are used, with some share of mixed franking on internal mail - here is a cover from a Russian philatelic phorum:

Yet, they are still not included officially into the system of the Post of Russia (just like the Crimea Post that is formally a separate business organization)/
A different thing are stamps from Transnistria - they really hardly see any postal use even inside that part of Moldova.