The time dependence of the fluorescence of solutions of 4-N,N-dimethylaminobenzonitrile (DMABN) and 3,5,N,N-tetramethyl-4-aminobenzonitrile (TMA BN) in neat polar solvents has been investigated, using a 25 ps UV-laser pulse for excitation and a streak camera for detection. Both the compounds DMABN and TMABN exhibit normal fluorescence F N and anomalous fluorescence F A, but all the solutions of TMABN show merely a single band in the fluorescence spectrum, which is a superposition of the bands F N and F A. In the case of DMABN the fluorescence in the region λ < 400 nm, where F N dominates, the fluorescence decays tri-exponentially due to fluorescence from three types of species, namely excited solute-solvent complexes, excited bare solutes and solute-solvent exciplexes. Within the lifetime of these emitting species there is probably no reverse reaction from exciplexes to excited solute-solvent complexes or excited bare solutes. This is in contrast with a previously presented picture, which includes such a reverse reaction. In the case of the solution of DMABN in n-butanol, the fluorescence at λ < 400 nm is bi-exponential. We show that this is due to an accidental degeneracy of two lifetimes. In contrast to a previous conclusion, we find that DMABN exists partially in the form of ground state solute-solvent complexes also in the solution in nitriles. The anomalous fluorescence develops in two phases, in the first one solute-solvent exciplexes are formed and in the second one the dielectric polarization of the solvent around the exciplex builds up. The rate constant for the formation of the anomalously fluorescing species, i.e. solute-solvent exciplexes, bears no relation with the longitudinal relaxation time, as claimed to have been shown previously.