Spetsnaz is an umbrella term for any special forces in Russian, literally meaning "special purpose forces". These Russian special forces can specifically refer to any elite or special purpose units under subordination of the Federal Security Service (FSB) or Internal Troops of Russian Ministry of Internal Affairs, and the units controlled by the military intelligence service GRU.
In Predator, Spetsnaz personnel appear as Soviet military advisors to the guerrilla forces in the Republic of Val Verde and one of them is seen executing a CIA agent with his pistol. Before facing the Yautja, Dutch and his team would later completely destroy their encampment and massacre almost the entire enemy presence, including the Russian advisors, leaving only Anna as their prisoner.
These two films are the only appearances (so far) of this force in the series.