It is well known that in plasmas with &bgr;=(vs/vA)2<1 (vs is the ion acoustic velocity and vA is the Alfv¿n velocity), Alfv¿n waves propagating along an external magnetic field can have three kinds of parametric instabilities: ordinary decay instability, beat wave instability, and modulational instability. However, when &bgr;≥1, there is only a beat wave instability, although decay and modulational instabilities are also possible from the point of view of the resonance conditions. When &bgr;≲1, there is, in general, a beat wave instability, but a modulational and a decay instability can also occur for some values of the pump wave amplitude. It is shown here that damping effects can destabilize regions that are stable under nondissipative fluid theory. This is done by using only fluid theory. Landau damping effects on the ion acoustic modes are simulated by a collisional-like term in the longitudinal component of the fluid equations. It is shown that when there is only a beat wave instability, damping effects can destabilize modulational- and decay-type instabilities. When there is a beat wave and a modulational instability, damping effects destabilize the region where one could expect a decay instability. The modulational-like instability is shown to trigger a forward propagating Alfv¿n wave. On the other hand, the decay-like instability generates backward propagating Alfv¿n waves. These results are in agreement with hybrid kinetic-fluid approaches and hybrid simulation codes. ¿ 2000 American Geophysical Union