X-irradiation of nonpolar solutions likely provides a possibility to create exciplexes for any donor-acceptor pair that would energetically and sterically allow this. Thorough study and characterization of X-radiation generated exciplexes usually cannot be carried out with conventional methods because of the complex and non-exponential formation and decay dynamics of these species. In this paper, we present a simple and universal experimental approach for the estimation of fluorescence lifetimes (τF) of X-radiation generated exciplexes. The suggested procedure is based on the comparison of quenching of the exciplex emission band and the emission band from a standard luminophore with a known excited state lifetime by dissolved oxygen. Using this approach we report the τF values for two systems with optically inaccessible exciplexes, diphenylacetylene-N,N-dimethylaniline (DMA) and p-terphenyl-DMA, and for two typical exciplex forming systems, naphthalene-DMA and anthracene-DMA. All the found τF values for the X-radiation generated exciplexes lie in the range of 50-70 ns. The accuracy of this approach was checked by time-resolved measurements under X- or near-UV irradiation for those pairs, whose properties make this feasible. The proposed method gives a possibility to avoid a complex numerical evaluation of the non-exponential kinetics of recombination luminescence, and can be used to estimate the characteristic τF values for luminophores and excited complexes formed under X-radiation.