Detailed stationary photoionization models with homogeneous chemical composition were constructed for a bright filament of the Crab Nebula centered ~42″ W-SW of the pulsar. So far this filament is the only one which has been observed in the ultraviolet (Davidson et al, 1982), in the visual (Miller, 1978; Davidson et al, 1982) and in the near-infrared (Dennefeld and Péquignot, 1982), so that numerous constraints and meaningful tests of the models exist. On the other hand the computer program used in the calculations includes recently introduced atomic physics processes (charge exchange reactions and “low-temperature” di-electronic recombinations) and was tested and calibrated by means of models of the high-excitation planetary nebula NGC 7027 whose line spectrum shares some characteristics with that of the Crab Nebula.