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This paper derives exact expressions for the level crossing rate and average fade duration of multibranch pure-selection, equal-gain, and maximal-ratio combiners operating over independent non-identical α-μ (also called generalized Γ or Stacy) fading channels. The derived expressions are in closed form for pure-selection combining and in integral form for equal-gain and maximal-ratio combining. For the two latter schemes, accurate closed-form approximations are then provided. The analytical results are validated by reducing the general expressions to known particular cases and, more generally, by means of simulation. Numerical examples are also given to illustrate the high accuracy of the proposed closed-form approximations.