Currently 18 hereditary neurological diseases are known to be associated with such mutations as multiple insertions of a single amino acid into the protein sequence. Therefore, investigation of the functional purpose of simple amino acid motifs becomes an important biological task. In this work, we studied the frequencies of motifs consisting of six identical amino acids and of simple six-amino-acid motifs consisting of two randomly located amino acids. The investigation was conducted on three eukaryotic proteomes of the wellstudied model organisms, Homo sapiens, Drosophila melanogaster, and Caenorhabditis elegans. We showed that many simple motifs occurred very frequently; the data on the frequency were presented at http://antares.protres.ru/motifs_six_residues.html. These results suggest such motifs to be responsible for common functions of non-homologous and unrelated proteins in different organisms.