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In this paper, we study the phase and amplitude instability mechanisms of midinfrared quantum-cascade lasers with Fabry-Perot cavity. The phase instability exhibits the single-mode nature and the amplitude instability is the multimode Risken-Nummedal-Graham-Haken kind of instability. The stability analysis is performed based on the nonlinear Maxwell-Bloch formulism. The phase instability and amplitude instability are decoupled based on the symmetry and antisymmetry of propagating modes in the cavity. We also discuss the influences of Kerr nonlinearity from optical transitions on these instability mechanisms. The Kerr nonlinearity exhibits as the combination of saturable absorber effect in the transverse direction and the self-phase modulation (SPM) in the longitudinal direction. The saturable absorber could lower the threshold of both instability mechanisms. The SPM has an impact on the instability spectra of quantum-cascade lasers. It could not only broaden the unstable frequency domain, but also transform it from the single-mode to the multimode domain.