Abstract Additional waves of exciton polaritons are studied in thin (1.5–1.8 μm) CuGaS 2 crystals at 9 K. The reflectivity spectra show a fine structure related to the interference of Fabry–Perot and additional waves which is a consequence of the polariton spatial dispersion. The main parameters of the exciton polaritons were determined from the spectra calculations. The Γ 4 excitons of big oscillator strength are shown to excite the additional polariton waves of the Γ 5 excitons of small oscillator strength, which interfere determining the fine structure in exciton resonance optical spectra.