A class of parametric instabilities of large-amplitude, circularly polarized Alfven waves is considered in which finite frequency (dispersive) effects are included. The dispersion equation governing the instabilities is a sixth-order polynomial which is solved numerically. As a function of K ≂ k/ko (ko and k are the wave number of the ''pump'' wave and unstable sound wave, respectively), there are three regions of instability: A modulation instability at K1, and a relatively weak and narrow instability at K≂1. As a function of B ≂ cx2/vA2 (where cs and Va are the sound and Alfv¿n speeds, respectively), the modulational instability occurs when &bgr;1) for left-hand (right-hand) pump waves, in agreement with the previous results of Sakai and Sonnerup (1983). For &bgr;≤1, dispersive effects tend to enhance the decay instability for right-hand waves and to reduce it for left-hand waves. For &bgr;≥1 this tendency is reversed. For right-hand waves the decay instability is dominant for &bgr;≤1, while the modulation instability dominates for sufficiently high &bgr;. The growth rate of the decay instability of left-hand waves is greater than the modulational instability at all values of &bgr;. Applications to large-amplitude waves observed in the solar wind, in computer simulations, and in the vicinity of planetary and interplanetary collisionless shocks are discussed.