The theme of this study is the explanation of cultural development in the term of Darwinian evolutionary theory. The author concerns himself with meme theory (memetics) and the arguments of its critics, and seeks to evaluate some of them. He considers the current state of scientific discourse regarding the application of Darwin's theory of natural selection to cultural evolution. The concept of natural selection, however, is not an essential part either of evolutionary theory or of its application to culture. Hence, the author also gives attention to so-called neutral evolution. On the conclusion of his study he considers the emergence of new cultural variants and their preservation in memory systems depending on concrete socio-cultural conditions. In this respect for cultural evolution is distinguished fundamentally from the classical evolutionary models. The algorithm of natural selection (heredity, variability, selection) is only one of the mechanisms to which cultural evolution is a subject. Cultural development therefore cannot be modelled only by means of natural selection, but at the same time it would be a mistake to exclude it from this model.