The matrix Integral Encounter Theory (IET) and its modified version (MET) developed earlier are used to study the kinetics of the reversible transitions between two metastable (as singlet and triplet) states of the fluorescent particle. Induced by binary encounters with inert catalysts, these transitions result in either (a) energy quenching or (b) energy conservation, depending on what lifetime of these two states is longer. Integral encounter theory describes adequately the kinetics of energy conservation followed by delayed fluorescence while differential or Markovian versions of the same theory fail. Another advantage of the IET is the natural accounting for arbitrary strong light pumping which makes the Stern-Volmer constant dependent on light intensity, differently for cases (a) and (b). (C) 2001 American Institute of Physics.