lnfrared transmission and reflectance measurements are made on single crystals of the layered compound ZnIn,S, with C& structure in the range between 4000 and 33 em-,. According to group-theoretical analysis there are altogether 6A, + 6E zone centre optical modes which are both ir-and Raman-active. 4A1 + 4E modes should be intralayer modes, the remaining 2A, + 2E ones should be rigid layer modes with distinctly lower frequencies. The number of observed onephonon frequencies is found to be by far larger than expected. 16 frequencies of ZnIn,S, are found t o coincide very well with frequencies of certain critical-point phonons of cubic ZnS and with certain phonon frequencies of @-In&, respectively. The "additional" frequencies related to the number of frequencies predicted by group theory, which occur in the ir spectrum, are believed to arise from broken translational symmetry of the lattice.