Now it is known that 18 neurological inherited diseases connected with mutations of multiple insertion of one amino acid residue in protein sequence. Therefore, studying the functional role of such simple motifs is an important task in biology. In this work we have investigated how often homorepeats, i.e. runs of a single amino acid residue, of 6 amino acid residues long as well as simple motifs consisting from two amino acid residues of 6 residues long situated in any position occur in three eukaryotic well studied proteomes: Homo sapiens, Drosophila melanogaster, Caenorhabditis elegans. It turns out that many simple motifs occur very often. The occurrence for each motif can be found at our site: http://antares.protres.ru/motifs_six_residues.html. One can suggest that such short similar motifs are responsible for the common functions for nongomologous, unrelated proteins from different organisms.