The German army had a number of special forces, most of which are best described by the French term hors de ligne, that is "outside of the regular army." Foreign troops have always fallen into this category in every army and the Germans certainly ended up with a tremendous force of foreign soldiers fighting in their uniforms. However, the Germans had three other non-traditional forces in their army.
The first, the Waffen SS, sprang from Hitler's personal bodyguard and much like many other Guard forces in the world's long military history, developed into a completely independent army all unto itself. Though not intentionally, it most assuredly falls into a category quite similar to that held by Napoleon's Imperial Guard, whose roots also are found in a dictator's personal bodyguard. Unlike the Imperial Guard, which was Napoleon's favored children, the SS belonged not to Adolf Hitler, but to Heinrich Himmler, Reichsführer der SS. It was not only a field force, but a tool in the internal political struggle between Hitler's cronies.
The SS also, like Napoleon's Imperial Guard, contained large numbers of foreign troops. In contrast to Napoleon's Imperial Guard, however, the SS went on a massive recruiting effort among foreign nationals in an effort to make it as large as possible. And, also unlike Napoleon's Imperial Guard, the German portions of the SS were subjected to an ideological mania for racial purity that was frequently swept aside when it was convenient. Large portions of the SS contained non-Germanic troops. Much of the SS fought with a steadfastness that was found in Napoleon's Old Guard, while some parts formed with foreign nationals had very poor reputations that included mass desertions, mutiny, and atrocity.
The second portion of forces hors de ligne in the German army was the Luftwaffe ground troops. The German division of operations between the army, navy, and air force was contorted by personalities and the political power base on which the Reich was formed. Hermann Goring claimed and was given anything that had any involvement with flying. As a result, the German paratroopers or fallschirmjägers, were part of the Luftwaffe. Operationally they were handled by the Army, but they were Goring's toys to play with as he wished. Like the SS, however, they also developed a ferocious reputation as fanatical fighters and were greatly feared and respected by their enemies.