One the most controversial problems of the Middle Palaeolithic research is the origin of symbolic behavior and who was responsible – only populations of anatomically modern humans (Homo sapiens in Africa) or also populations of Neandertals in Western Eurasia? According to the current evidence, there are two opposite concepts. The first one assumes that use of complex stone and bone technology, burying their dead, and making of art objects as well as personal ornaments originated with anatomically modern humans. The second one supports a view that the Neandertals developed their culture in a similar way, convergent or in various contacts with the societies of early Homo sapiens. Their technological equipment enabled them to enter and colonize new areas in northern latitudes, which was impossible without developed knowledge about fire usage, shelter building, and adequate clothing. Neandertals made efficient tools, including composite tools made of various raw materials. In addition, the social relations of Neandertals exemplified an altruistic approach to others. According to the current knowledge, the origin of symbolic behavior cannot be linked only with anatomically modern humans or any isolated Middle Paleolithic population. It appeared much earlier, in the Lower Palaeolithic. It is necessary to remember that archaeological data for remote time are still rare and more evidence is needed to test concepts.