The energies and lifetimes of magnons in several Mn-based Heusler alloys are studied using linear response density functional theory. The number of the spin wave branches in Co₂MnSi corresponds to the number of its magnetic sublattices in contrast with the NiMnSb case in which the induced Ni sublattice cannot support optical magnons. The half-metallicity of these systems results in long-living acoustic spin waves. The example of non-half-metallic Cu₂MnAl shows that the hybridization with Stoner continuum leads not only to the damping of magnons but also to a renormalization of their energies.