The conditions for either stable or oscillatory combustion are determined analytically for a burning mixture of ideal gases in an annular combustion zone. The mixture, flowing steadily in the axial direction, is perturbed by a small-amplitude, tangentially propagating pressure disturbance. The rate of energy release is described by an Arrhenius function. The stability of the system is governed by an amplif cation coefficient that reflects the effects due to the rate of energy release and the convective transport of energy. The stability criterion is employed to evaluate the effects of changes in the system parameters on the combustion stability. A critical value of the Arrhenius exponent is determined which exists at a line demarcating regions of stable and oscillatory combustion; it is a function of the flowfield variables, the specific-heat ratio, and the reaction rate frequency factor. A partial, qualitative verification of the stability trends predicted by the analysis is provided by the known stability behavior of premixed gases burned in cylindrical and annular combustors.Mach number m = mean molecular weight n = wave number for tangential mode of oscillation p -static pressure p i} p. 2 = amplitude constants r = mean radius of annulus, radial coordinate R -gas constant R u -universal gas constant t = time T = static temperature v = velocity vector v$j v z = tangential and axial velocity components, respectively Xij Xj = mass fractions of components i and j z = axial coordinate & = na/r Sij 5 2 = constant phase angles e = activation energy 0 = angular coordinate p = density