A new theoretical approach is proposed to explain the nature of the well-known narrow and intense optical J-band of J-aggregates of polymethine dyes. The old approach proposed by Franck and Teller in 1938 and based on the Frenkel exciton theory does not take into account the specific properties of the main optical chromophore of polymethine dye monomers—the polymethine chain. In the new approach proposed by Egorov and based on a new fundamental physical theory—quantum‒classical mechanics, which takes into account the chaotic and regular dynamics of the transient state, the optical properties of the polymethine chain and monomers as a whole are considered as a key factor determining the unique optical properties of J-aggregates. The J-band is explained by the so-called Egorov resonance, the presence of which follows from quantum‒classical mechanics. Many other experimental facts have also been explained on the basis of quantum‒classical mechanics. These include: asymmetry of the shape of the luminescence bands of J-aggregates relative to their optical absorption, an anomalously small Stokes shift of the J-band; the shape of the optical bands of dimers, H- and H*-aggregates; strong detuning of the Egorov resonance during the transition from one-photon to two-photon absorption. The conditions for the restoration of the Egorov resonance during two-photon absorption are predicted.