We have studied the theoretical properties of electromagnetic ion cyclotron (EMIC) waves which occur in the plasma depletion layer. Our analysis assumes a homogeneous plasma with the characteristics which were measured by the AMPTE/CCE satellite at 1450--1501 UT on October 5, 1984. During the time, waves were observed in the Pc 1 frequency range (0.2--5 Hz) below the hydrogen gyrofrequency, and we identify these waves as EMIC waves. In agreement with observations, the theory predicts two frequency bands of waves, above and below about 0.4 &OHgr;H, where &OHgr;H is the hydrogen gyrofrequency. The higher-frequency instability is driven by the temperature anisotropy of the H+ ions, while the lower-frequency instability is driven by the temperature anisotropy of the He2+ ions. These two frequency bands occur on the same dispersion surface. The EMIC waves tend to quasi-linearly control the value of the proton temperature ratio T⊥/T∥ by an increase in T∥ due to scattering so that the bulk plasma stays near marginal stability. Here, T∥(T⊥) is the temperature parallel (perpendicular) to B0. Without convective effects, the nonlinear wave amplitude tends to be large over the entire angular range 0≤&thgr;kB≤75¿, where &thgr;kB is the angle between the wave vector and the background magnetic field (B0). However, waves for which the perpendicular (to B0) group velocity vg⊥ is large, are likely to be convectively limited in growth. Within the higher-frequency band, vg⊥ is small only for wave vectors k which are close to parallel to B0. Within the lower-frequency band, vg⊥ is small only for oblique k. Therefore, it is likely that the higher-frequency waves will have k roughly parallel to B0 and will be left-hand polarized, while the lower-frequency wave band will have k oblique to B0 and will be linearly polarized, in agreement with observations. ¿ American Geophysical Union 1993