It is shown that finite amplitude electrostatic ion cyclotron (EIC) waves can parametrically decay into daughter EIC waves and kinetic Alfvén waves. Since the current associated with the latter is d.c. in the EIC time scale, it can linearly excite EIC waves when the amplitude of the Alfvén waves is sufficiently high. This provides a mechanism for the simultaneous existence of EIC and Alfvén fluctuations. Application of the theory in the auroral zone of the ionosphere is discuss