The competence of the reversible exciplex formation and parallel quenching of excitation (by electron or energy transfer) was considered using a non-Markovian pi-forms approach, identical to integral encounter theory (IET). General equations accounting for the reversible quenching and exciplex formation are derived in the contact approximation. Their general solution was obtained and adopted to the most common case when the ground state particles are in great excess. Particular cases of only photoionization or just exciplex formation separately studied earlier by means of IET are reproduced. In the case of the irreversible excitation quenching, the theory allows specifying the yields of the fluorescence and exciplex luminescence, as well as the long time kinetics of excitation and exciplex decays, in the absence of quenching. The theory distinguishes between the alternative regimes of (a) fast equilibration between excitations and exciplexes followed by their decay with a common average rate and (b) the fastest and deep excitation decay followed by the weaker and slower delayed fluorescence, backed by exciplex dissociation.