The transmission spectra of GaSe and GaS crystals of different thicknesses prepared by mechanical stratification of bulk crystals have been investigated. The quantum-size shifts of exciton resonances in thin GaSe samples are as high as 12 meV, which is close to the exciton binding energy. The high-energy interband transitions in GaSe and GaS are observed near 3.4 and 3.7 eV, respectively.