An extension of the cluster-(quadrupole-octupole) phonon model is proposed for nuclei with A~90 to describe simultaneously positive-and negative-parity states, in which quadrupole as well as octupole vibrations of the SSSr core are allowed. The cluster states include particle and particle-hole core excitations. The residual interaction is a delta-function force with spin-spin exchange plus a quadrupole-quadrupole force. The model is applied to STSr, 89Sr, SSy, and 90y nuclei. For each case, energy levels, spectroscopic factors, and electromagnetic properties are calculated and compared with experiment.Nuclear Structure: Theory, 87Sr, 89Sr, SSy, and 9Oy; calculated levels, J, 7r, S, q, #, and 7"1/2. Extended cluster-phonon model; quadrupole and octupole vibrations; particle and particle-hole core excitations.