The NOVA-K code is employed to study the effects of alpha particles on two types of magnetohydrodynamic (MHD) modes: (a) the stabilization of ideal MHD internal modes and the excitation of resonant internal modes, and (b) the alpha-particle destabilization of toroidicity-induced Alfvén eigenmodes (TAEs) via transit resonances. Analytical theories are also presented to help explain the NOVA-K results. The trapped alpha particles are found to destabilize the n = 1 internal mode and lower the total beta threshold. The circulating alpha particles can strongly destabilize TAE modes via inverse Landau damping associated with the spatial gradient of the alpha-particle pressure.