We report observation of strong phonon-pair oscillations in CdZnTe multiple quantum wells and cubic ZnTe(001). Using femtosecond laser pulses with photon energies far below the bandgap, the coherent phonon-pair oscillations are generated via the impulsive stimulated Raman scattering of the second order. Polarization- and phase-sensitive measurements allow us to resolve both relative Raman polarizabilities of various symmetry modes and their initial phases, simultaneously.