The excitation as well as relaxation dynamics of dye-doped nematic liquid crystal cells has been explored both experitnentally and theoretically. Overshoots in the build up of the probe signal diffracted from gratings written onto dye-doped liquid crystal systems have often been observed. The overshoot behaviour makes the accurate measurement of nonlinear optical (NLO) response magnitude difficult and ambiguous. Moreover, it complicates the understanding of the dynamics and the physics of the NLO processes. On, the basis of the system with trans-cis isomerisation as a mechanism of the NLO effect the quantitative model has been built to describe the experimental results which we observe. The two unknown material parameters: diffusion coefficient and cis species lifetime are calculated front the relaxation data. A quantitative model of the signal build-up uses these parameters. The calculated dynamic behaviour based oil this model correlates very well with the experimental data. The model is used to predict the performance of the system with various dopant diffusion properties.