It is demonstrated both analytically and numerically that mode couplings play an important role in the nonlinear evolution of alpha‐particle‐drivenlongwavelengthAlfve´n wave instabilities. The mode coupling process is characterized by a beat between two linearly unstable Alfve´n waves having opposite frequencies, which generates a linearly stable, static (zero frequency) mode. The backreaction of the static mode tends to stabilize the Alfve´n instabilities by eliminating the phase shift between the alpha pressure and the Alfve´n fluctuations.