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[en] In this review experimental results have been presented and analyzed, that are demonstrated an anomalous manifestation of the well-known for bulk crystals effect of exciton self-trapping in ordered molecular nanoclusters, so called J-aggregates. The main structure motive of the J-aggregates are weakly coupled 1D molecular chains in which electron excitations are existed as 1D Frenkel excitons. According to continuum theory of Rashba-Toyozawa only self-trapped excitons should exist in J-aggregate's because 1D excitons have to be barrierless self-trapped at any exciton-phonon coupling constant g = ε_L_R/2β, where ε_L_R - the lattice relaxation energy, 2β - the half-width of exciton band. By contrast, in experiments on the J-aggregates only emission of mobile free excitons was often ob-served. Using the Urbach rule for low-frequency edges analysis of exciton absorption spectra at low temperatures it was found that both weak (g < 1) and strong (g > 1) cases of exciton-phonon coupling could be realized in the J-aggregates. Moreover, it was experimentally demonstrated coexistence of free and self-trapped excitons in excited state of the J-aggregates at certain conditions, i.e. existence of the self-trapping barrier for the 1D Frenkel excitons. In the review it has been shown and analyzed reasons for the anoma-lous coexistence of the free and self-trapped excitons in the J-aggregates and demonstrated a control of exciton self-trapping efficiency in the J-aggregates through the constant g varying, which is principally impossible for the bulk molecular crystals. Using the exciton self-trapping phenomenon it has been discussed an alternative interpretation of wide band emission for some J-aggregates, which was explained in the framework of strongly localized exciton model.