In the paper is presented a possible classical explanation of the anomalous value ae = α/2π of the electron' and of the muon's magnetic moment, based on a vortexial pre-quantum model of electron and on the vortexial nature of the electron's magnetic moment resulted in the model as etherono-quantonic vortex: Γ * μ(r) = Γμ(rμ') + ΓB(r>rμ'), of ‚heavy' etherons (ms ≈ 10 -60 kg)-generating the magnetic potential A and of quantons (mh = h⋅1/c 2 = 7.37x10 -51 kg) -generating vortex-tubes ξB that materializes the B-field lines of the magnetic induction and a spinorial mass mμ of photons vortexed with the light' speed in the volume of radius rμ' = rμ 0 (1+ α/2π), (rμ 0 = ħ/mec). The value of the spinorial mμ-mass which explains the anomalous magnetic moment results almost equal but lower than the inertial mass me to which it not contribute, by the conclusion that the quantonic Γ * μ(r)vortex generates the inertial memass by photons confining with only a part ΔΓB of the ΓB-vortex, limited by a radius rl ≈ 3 √[2π/(2π-6)]⋅rμ', the mμ-mass explaining also the spin's value Sh ≈ ħ/2. The muon's and the proton's anomalous magnetic moments are expained by a composite fermion type of particle, with the e-charge given by an electron attached to a neutral cluster of magnetically paired quasi-electrons, with degenerate magnetic moment resulted by a degenerate Compton radius, i.e., decreased proportional with the density of particle's quantum volume in which is introduced the electron's superdense kernel.proportional with the density of particle's quantum volume in which is introduced the electron's superdense kernel.

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