Classical electrodynamics displays a formula for the equation of the motion of charged particles that has run away solutions. Gyarmati's wave approach leads to a solution fitting to the classical term in the low frequency regime. A shortage of the solution is that the characteristic time in the equation depends on the mass of the charged particle. An abstract model with two dynamic degrees of freedom results in a solution free of the above problem. For complete compatibility with electrodynamics, the need for a generalization of Maxwell's equations is probable.