Through a further application of the condition for magnetospheric wave growth in the presence of anisotropic charged-particle distributions, the Kennel-Petschek theory that traditionally imposes an upper bound on the integral flux at any energy above this threshold. Thus, a modest reformulation of the nonrelativistic Kennel-Petschek problem for electrons and protons enables a limiting energy spectrum to be derived, such that (for specified pitch-angle anisotropy s of the energetic particle population) electromagnetic-cyclotron waves at each frequency less than a fraction s/(s+1) of the equatorial gyrofrequency are marginally stable against spontaneous generation. The limiting spectrum is given in closed form for integer values of s (>0) and computed numerically or by analytical interpolation for non-integer values of s. Asymptotic expansions for energies E barely above and much greater than the minimum resonant energy E* provide estimates of the limiting energy spectrum J *4&pgr;(E) in these extremes, regardless of whether s is an integer. A reconsideration of the original Kennel-Petschek problem, in which the differential energy spectrum is not calculated but specified as a certain power law (J4&pgr; ∝ E1-l), enables both the wave frequency &ohgr;*/2&pgr; corresponding to maximum spatial growth rate and the limiting integral flux I *4&pgr; above the minimum resonant energy E* to be calculated in closed form as functions of l and s. ¿ American Geophysical Union 1988