The radiationless deactivation of the excited electronic states of the dual fluorescence molecule N-6,N-6-dimethyladenine (DMAde) was investigated using femtosecond time-resolved fluorescence up-conversion spectroscopy. The molecules were studied in solution in water and in dioxane. Fluorescence-time profiles were recorded in the wide wavelength range of 290 <= lambda(fl) <= 650 nm. The excitation wavelengths in the region of the first UV absorption band were tuned from close to the electronic origin (lambda(pump) = 294 nm) to excess energies of similar to 5400 cm(-1) above (lambda(pump) = 258 nm). Global fits to the measured curves turned out to reflect distinctive molecular relaxation processes on five well-defined time scales. Sub-100 fs and 0.52(3) ps lifetimes were found to predominate at the shortest UV and blue emission wavelengths in water, 1.5(1) and 3.0(2) ps components at intermediate wavelengths and a 62(1) ps value in the red region of the spectrum (2 sigma error limits of the last digits in parentheses). In dioxane, these lifetimes changed to <= 0.27 and 0.63(4) ps in the UV, 1.5(1) and 10.9(10) ps in a wide range of intermediate, and 1.40(4) ns at the longest wavelengths. However, little dependence of the respective time constants on lambda(pump) was observed, indicating that the ensuing relaxation processes proceed via practically barrierless pathways through conical intersections. Building on the knowledge for the parent molecule adenine (Ade), the observations were rationalized with the help of a modified four-state model for the electronic dynamics in DMAde with the pi pi*(L-a), pi pi*(L-b), and n pi* states similar to those in Ade and an intramolecular charge-transfer (ICT) state, which has no counterpart in Ade, responsible for the long-wavelength fluorescence.