Equations of non-ideal Alfvén eigenmodes in stellarator plasmas are derived that take into account the finite ion Larmor radius, the parallel perturbed electric field and dissipative mechanisms. On the basis of these equations, it is shown for the first time that there exist kinetic mirror-induced Alfvén eigenmodes—modes associated with the presence of the mirror Fourier harmonic in the equilibrium configuration (the harmonic that dominates the magnetic field of the optimized stellarators of the Wendelstein line). Destabilization of these modes by fusion-produced α-particles in a Helias reactor is considered.