Alpha-particle populations can significantly alter existing magnetohydrodynamic (MHD) instabilities in tokamaks through kinetic effects and coupling to otherwise stable shear Alfvén waves. Resonances of the trapped alpha-particle precessional drift, with the usual ballooning mode diamagnetic frequency (ω*i/2) and the toroidicity-induced Alfvén eigenmode (TAE), are considered. These are examined for noncircular tokamaks in the high-n ballooning limit using an isotropic alpha-particle slowing down distribution and retaining the full-energy and pitch-angle dispersion in the alpha-particle drift frequency. Applying this to the Compact Ignition Tokamak (CIT) and the International Thermonuclear Experimental Reactor (ITER) indicates that ballooning instabilities can persist at betas below the ideal MHD threshold. These are especially dominated by the destabilization of the TAE mode. In addition, a hybrid fluid-particle approach for simulating alpha-particle effects on pressure-gradient driven instabilities is described.