The dynamics of a solid-state laser sustaining the oscillation of two orthogonally polarized eigenstates and passively Q switched by a Cr4+:YAG (YAG denotes yttrium aluminum garnet) saturable absorber is experimentally investigated. A set of rate equations in which the orientation-dependent interactions between the intensities and the saturable absorber have been taken into account is developed to describe theoretically the evolution of such a laser. When a [001]-cut Cr4+:YAG plate is used, orthogonally polarized pulsed eigenstates are emitted either successively or simultaneously, depending on the orientations of the eigenstates with respect to the crystallographic axes. Namely, in the latter case, beat note carrying pulses are emitted, whose beat frequency is continuously tunable. On the other hand, when a [111]-cut Cr4+:YAG plate is used, the simultaneity regime is never observed. All experimental results, obtained using a diode pumped Nd:YAG laser, are well confirmed by the theoretical model. [S1050-2947(99)02111-3].