The inliuence of the polariton effects on the internal structure of an excitonic molecule (xx) is examined by the solution of the new xx Schrodinger equation which includes the polariton effects self-consistently.In 3D (CuC1) the radiative renormalizations yield a nonparabolic xx dispersion with infinite effective xx mass at zero momentum; in quasi-2D (GaAs) they give rise to a "Mexican hat" structure in the xx dispersion at small momenta together with a considerable increase of both the xx binding energy e and the inverse xx radiative lifetime I . In quasi-1D the inAuence of the polariton effects is so strong that the xx exists only as a broad resonance (e" -I "'). PACS numbers: 71.35.+z, 71.36.+c Radiative corrections are well known in atomic physics due to the Lamb shift [1]. This shift of a transition frequency of an atom in the photon vacuum is due to spontaneous emission. It can be calculated within perturbation theory. We report here radiative renormalizations for an excitonic molecule in direct-gap semiconductors. These renormalizations originate from the polariton effect and cannot be included perturbationally. They give rise to the significant observable modifications of the xx dispersion for all dimensions: D = 3 (bulk semiconductors), D = 2 [quasi-2D quantum wells (QWL)] and D = 1 [quasi-1D quantum wires (QWR)].Novel high-precision techniques with a spectral resolu-tion~10 p, eV have been applied to reinvestigate an xx in bulk CuC1 [2]. Recently, the xx has been observed also in QWL [3,4]. The xx ground state has been calculated variationally within the underlying electron-hole (e-h) picture for 3D [5], 2D [6], and 1D [7] cases, respectively.The exact interparticle Coulomb potentials have been included, while the polariton effects have been neglected completely.The xx radiative decay is then treated perturbationally as a direct optical conversion xx~exciton (x) + photon (y) with a giant oscillator strength [8]. The strong interaction with the electromagnetic field will, however, also modify the xx dispersion and give rise to an xx Lamb shift 5The e-h picture can be reduced to the x representation (see, e.g. , [9,10]), if the x binding energy e' is much larger than that of molecule e . This approximation holds, e. g., for bulk CuC1 (e' = 190 meV and e" = 34 meV) and for GaAs QWL (e' = 10 meV and e" =