A theory of excitons in semiconductors in the Fractional Quantum Hall (FQH) Effect regime is presented. Non-conventional properties of magnetoexcitons in this regime originate from the fact that elementary excitations of the FQH phases carry fractional charges. Properties of excitons strongly depend on the separation h between electron and hole confinement planes. When this separation is not too small, h 2 I , where 1 is the magnetic length, excitons look like quasiatoms consisting of a valence

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... hole and several fractional charges. Charge fractionalization results in a multiple-branch structure of the exciton energy spectrum. Symmetry classification of the branches is proposed, and their relation to the low-energy part of the Hilbert space of the charged elementary excitations of the FQH phases is established. Spectroscopic implications of the spectra classification, including the selection rules, are discussed.