That depends a little bit on your definition of an elite unit. If we assume an elite unit is a high prestige military formation with strict recruitment standards (or at least more demanding than other units), and specialized training, then the East German Luftsturmregiment 40 (literally: "air storm regiment") would be a good candidate.

The LStR-40 was the airborne force of the East German Nationale Volksarmee ("National People's Army", abbreviated as NVA). Doctrine and mindset of the NVA was closely modeled on the Soviet Armed Forces. The Soviets highly valued large, separate airborne formations as quick reaction force and for commando warfare. In case of all-out war with NATO airborne troops would be placed deep into enemy territory and tasked with the occupaton of key locations, diversion of forces, disruption of enemy logistics etc. The East German LStR-40 was trained to fulfill such tasks alongside the (much more numerous) Soviet airborne troops.

The East German Ministerium für Staatssicherheit ("ministry for state security"), better known by its abbreviation Stasi, maintained its own special forces branch, the rather unspectacularly named Arbeitsbereich des Ministers Aufgabenbereich "S" (AGM/S in short, the "S" stands for Sonderfragen, "special tasks"). The AGM/S was responsible for special operations behind enemy lines like sabotage, guerilla warfare, and stay behind operations in case of enemy occupation. Its mission is described here in its own working paper in German if you're interested. Inside the German Democratic Republic, the AGM/S served as a counter-terrorism unit.

I can't say much about Polish units, I'm afraid. My military knowledge is fairly limited.