A small-perturbation investigation of ammonium perchlorate deflagrations is made to determine the intrinsic stability of a one-dimensional burning configuration. It is found on the basis of a particular model of the flame structure that above a certain pressure, dependent upon the numerical values used, a stable one-dimensional flame cannot exist. Detailed calculations are presented for a preferred set of parameters, and the pressure above which stability is impossible is between 620 and 2140 psia, depending on whether the AP-gas interface is in equilibrium or is pyrolysis controlled.