In this paper we consider the problem of the radiative decay of electronically excited states of a large molecule. We have considered both intramolecular vibronic coupling and the interaction with the radiation field. Compound states for a system of decaying indistinguishable levels are constructed using the Fano method. General expressions for the radiative decay rate are derived and applied for the statistical limit of intramolecular vibronic coupling. On a time scale shorter than a typical intramolecular recurrence time the radiative decay is exponential, and the reciprocal lifetime consists of independent contributions of radiative and nonradiative components. The experimental implications of these results for large and medium size molecules are discussed.