Relaxation of elementary excitations with small wave vectors (magnons) in the nematic phase of magnet with spin S = 1 near antiferromagnetic SU(3) critical point has been studied. In the vicinity of the critical point the dispersion law minimum appears near the border of Brillouin zone. The elementary excitations near this minimum (rotons) have the gapped dispersion law, their damping is high, and they essentially influence on the relaxation of magnons. The roton contribution to the damping of magnons is strong both at the critical point and close to it
