A ZELDOVICH-NOVOZHILOV model for the pressurecoupled response of solid propellants was developed with heat conduction in the condensed phase governed by a relaxation time, non-Fourier relation. Results indicate that, although the relaxation time appears in a frequency-squared relaxation time product combination, the non-Fourier model has negligible effect on the response in the frequency domain of interest to combustion instability for reasonable values of relaxation time. For large values of this parameter, the resonance is shifted to lower frequencies, reduced in magnitude, and narrowed. Presented as Paper 82-1102 at the AIAA/SAE/ASME 18th Joint Propulsion Conference, Cleveland, Ohio, June 21-23, 1982; submitted June 25, 1982; synoptic received July 5, 1983. Copyright © American Institute of Aeronautics and Astronautics, Inc., 1982. All rights reserved. Full paper available from AIAA Library, 555 W. 57th Street, New York, N.Y. 10019. Price: Microfiche, $4.00; hard copy, $8.00. Remittance must accompany order. * Graduate Student, School of Aeronautics and Astronautics (currently, Engineer, Morton Thiokol, Inc., Huntsville, Ala.). Student Member AIAA. tSenior Researcher, School of Aeronautics and Astronautics. Associate Fellow AIAA.