(covers information from several alternate timelines)
The Wehrmacht was a German-derived expression commonly used on Earth in the 1930s-1940s to indicate the combined regular German military, consisting of the army (Heer), navy (Kriegsmarine) and air force (Luftwaffe) of Nazi Germany, not including the armed ground forces (Waffen-SS) of the Nazi Party's own "Schutzstaffel" (SS) force. Its emblem was in German parlance called "Balkenkreuz" (translated as "beam cross"), and was carried on all vehicles of the organization on Earth, as well as on those of its 23rd century derivative on the planet Ekos.
Alternate timeline Wehrmacht Edit
In an alternate 1944 caused by the Temporal Cold War, the Wehrmacht, alongside the SS, was able to conquer Europe and the eastern seaboard of the United States. Their occupation was fiercely fought against by the American Resistance. The resistance ambushed a small prisoner convoy that consisted of an Ford Model 51 truck that transported Captain Jonathan Archer from a field hospital for questioning, and escorted by a BMW R75 motorcycle and a Wehrmacht Volkswagen Kübelwagen (though driven by a SS soldier), carrying the license plate "WH-52552". All vehicles were damaged during the attack and their German occupants killed. (ENT: "Storm Front")
Concurrently, a Wehrmacht Generalmajor, arriving in a Sd.Kfz. 251 half-track vehicle, was stationed at the occupied American White House as liaison officer in order to relay orders from Adolf Hitler to the Na'kuhl, who were purportedly developing advanced weaponry for Nazi Germany. Under orders to provide the Na'kuhl with resources, the misguided general belatedly realized that they were following their own agenda and was subsequently killed by the Na'kuhl leader Vosk. (ENT: "Storm Front", "Storm Front, Part II")
Ekosian Wehrmacht Edit
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In the mid-2200s, the historical German Wehrmacht was recreated on the planet Ekos as a result from an ill-advised attempt by historian John Gill to reform Ekosian society, which was in the throes of anarchy, along the lines of a modified form of National Socialism. Originally dispatched by the Federation to serve as a cultural observer only, and in clear breach of the Prime Directive, Gill believed that by establishing a passive version of the Nazi state, but complete with such organizations as the SS, Wehrmacht and their accouterments – resulting in a severe case of cultural contamination – , he could quell the upheaval on Ekos, setting himself up as Führer after his role model, Adolf Hitler.
However, with power surreptitiously usurped by Deputy Führer Melakon, Gill's social experiment quickly went awry and started to emulate what had happened on Earth in the 1930s-1940s. In 2268, a publicly shown newsreel showed Ekosian Wehrmacht armed forces gearing up for an aggressive campaign against the Zeons, immigrants from the neighboring planet Zeon, and by that time a much persecuted minority. Shortly thereafter a solitary Ekosian Wehrmacht Generalmajor was present at a rally, a bit lost amidst a crowd of party, and SS officials, where Melakon and Gill presented their "Final Decision" for the "Zeon problem".
Interference by the Ekosian and Zeon underground alliance, aided by the crew of USS Enterprise who were sent to Ekos to investigate, resulted in the death of the two Führers and their intentions were thwarted for now. However, it is not known whether or not the Wehrmacht and SS organizations continued to exist on Ekos afterwards. (TOS: "Patterns of Force")
Background information Edit
Though the expression "Wehrmacht" (translated as "defense force") was, and is, almost universally used, even among Germans themselves, to indicate the army branch, its proper usage was to denominate the entirety of the regular (as opposed to the SS; see background note for that organization) German military, thus including the air force ("Luftwaffe") as well as the naval forces ("Kriegsmarine" or "Marine" for short). The correct German word for army is "Heer" and the correct full, official and bureaucratic usage is "Wehrmacht Heer", hence the "WH" on the license plates carried by their vehicles ("WL" and "WM" respectively for the other two branches, and, obviously, "SS" in runic script for that organization).
While the Ekosion general was a clearcut reference to the Wehrmacht, the references in the Ekosian newsreel were more tentative, though still there nevertheless. The reel contained especially produced footage for the episode, intercut with clippings of actual, historical German news, or propaganda footage. In the late 1930s prior to the outbreak of World War II, the military branch of the SS, the Waffen-SS, was at the time still very small and as "amateurs" despised by the regular German military. Developing somewhat sequestered from German society and military alike in that era, they, excepting two very limited and near unnoticed, small unit actions in the 1938 "consensual" Austria and Sudetenland annexations (actually meant to be their baptisms as a military unit), did not partake in any open military maneuvers until the September 1939 Polish campaign, the actual start of the war. The above and other featured parading soldiers in the reel, lacking any discernible SS insignia (on the uniform collars in particular), were from a newsreel of the April 1940 Wehrmacht occupation of Denmark, and in which the Waffen-SS had not taken any part. 
The tank clipping, shot in either Belgium or northern France during the May 1940 Blitzkrieg campaign in the West, unequivocally showed Wehrmacht tanks. The very first SS tank unit only became operational at the start of 1942, well into the war. As a privileged part of the Nazi party, the SS was given preferential treatment, and had first pick of the very best and most modern weaponry German manufactures had to offer at any given time, which the tanks featured in the reel – two SdKfz 265 Panzerbefehlswagens and a Panzer I tank – were most definitely not. Already obsolete at the start of the war, both machines were by 1942 in an advanced state of being phased out for operational duties, and neither had ever served with any SS armored unit.
World War II-era German soldiers were in the Star Trek television franchise, aside from "Patterns of Force" and the two "Storm Front" episodes, also featured in the Star Trek: Voyager fourth season two-part episode "The Killing Game". But for reasons that can only be guessed at, Star Trek producers had, the two generals excepted, invariably chosen to portray only soldiers belonging to the SS. This seemed a bit incongruous as the Wehrmacht had been the larger organization by far (enlisting approximately 18 million soldiers during its existence, whereas the SS in its entirety, non-combat units included, had comprised of approximately 1.2 million volunteers), having carried the brunt of both combat, as well as occupation duties. The Kübelwagen and the general in the two "Storm Front" episodes, as well as the more ephemeral references in "Patterns of Force", were the only allusions Star Trek has ever made to the regular German army. The SS counterpart of the Wehrmacht brigadier general would have been an "SS-Oberführer" or an "SS-Brigadeführer" – one of each actually seen in the by the Ekosion Generalmajor attended rally – sporting different insignia on both their uniforms and headgear.