Organic molecules with a small electronic gap between the S$_1$ and T$_1$ states (2000--4000 cm$^{-1}$) exhibit deviations from the exponential law of fluorescence attenuation associated with violation of the balance equation in the absence of collisions. This survey provides an exhaustive classification of all physical situations which arise in various correlations between parameters. Dephasing processes and the attenuation of molecular states, biexponential attenuation, and chaotic and periodic quantum beats in the limits of strong and weak coupling are discussed. The predictions of the strong coupling theory are compared with experimental data for pyrazine. Rotational effects are interpreted as a narrowing of a band of strongly coupled states with an increase in the rotational quantum number. Periodic quantum beats at the weak coupling limit arise due to a reversible energy exchange among vibrational sublevels.