An analytical model based on Volterra nonlinear functionals applied to semiconductor lasers has been developed. Analytical expressions are obtained for different laser diode responses, giving powerful tools for analysis. For harmonic input, the response is given including the gain compression factor ε. Second-harmonic distortion (2HD) shows two maxima at half relaxation oscillation frequency ΩR/2 and at ΩR, in agreement with experiments; the residual dc component due to nonlinearities is estimated and experimentally verified. Dynamic frequency deviation as function of bias current shows resonant characteristics. Relaxation frequency and damping rate ΓR reveal their precise dependence on ε and differential gain A. For step input, the turn-on delay ton and the overshoot PP/Pon expressions of our model are only functions of ΓR and ΩR. PP/Pon, and the ringing phenomena decrease with increasing bias current level