A two-mass model of vocal-fold vibrations is analyzed with methods from nonlinear dynamics. Bifurcations are located in parameter planes of physiological interest (subglottal pressure, stiffness of the folds). It is shown that a sufficiently large tension imbalance of the left and right vocal fold induces bifurcations to subharmonic regimes, toroidal oscillations, and chaos. The corresponding attractors are characterized by phase portraits, spectra, and next-maximum maps. The relevance of these simulations for voice disorders such as laryngeal paralysis is discussed.