It is well known that the temperature anisotropy of either the minority or majority species in a two-component plasma can make the electromagnetic ion-cyclotron mode unstable. This instability may be particularly relevant in tokamak experiments where high-power ion-cyclotron resonance heating (ICRH) is used to create an energetic population of minority ions. We investigate the nonlinear stability of this mode and show that it may decay by coupling with the sound waves supported by the two species or by a modulational decay into sideband waves.