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 this 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 ΩH, where ΩH 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 ≤ θkB ≤ 75°, where θkB is the angle between the wave vector and the background magnetic field (B0). However, waves for which the perpendicular (to B0) group velocity υg⊥ is large, are likely to be convectively limited in growth. Within the higher‐frequency band, υg⊥ is small only for wave vectors k which are close to parallel to B0. Within the lower‐frequency band, υg⊥ 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.