We had found nonreciprocity of spin waves in Pt/Co/Ir/Co/Pt synthetic ferrimagnets by Brillouin light scattering technique. It is shown that the main contribution to the nonreciprocity of spin waves is made by the Dzyaloshinskii-Moriya interaction with an energy density D ≈ 1.7 - 2.3 erg/cm2. The energy density of the Dzyaloshinsky-Moriya interaction in Pt/Co/Ir/Co/Pt synthetic ferrimagnets is higher than its values in heterostructures with one Co layer Pt/Co(1 nm)/Ir ~ 1.4 erg/cm2. The D value of synthetic ferrimagnets decreases with increasing thickness of the Co thin layer.