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We consider stability of solitons of 3D Maxwell--Lorentz system with extendedcharged spinning particle.The solitons are solutions which correspond to aparticle moving with a constant velocity $v\in\R^3$ with $|v|<1$ and rotatingwith a constant angular velocity $\omega\in R^3$.  Our main results are the orbital stability of moving solitons with $\omega=0$and a {\it linear} orbital stability of rotating solitons with $v=0$.  The Hamilton--Poisson structure of the Maxwell--Lorentz system is degenerateand admits the Casimir invariants. We construct the Lyapunov function as alinear combination of the Hamiltonian with a suitable Casimir invariant. Thekey point is a lower bound for this function. The proof of the bound in thecase $\om\ne 0$ relies on angular momentum conservation and suitable spectralarguments including the Heinz inequality and closed graph theorem.

On stability of solitons for 3D Maxwell-Lorentz equations with spinning particle