[en] A nonperturbative approach to the density-functional description of phase transitions in fluid composed of anistropic particles is presented. The theory is exact to second order in functional perturbation theory, and at higher orders satisfies all sum rules derived from density derivatives of the two-point direct correlations. The authors have applied this theory to orientational and translational freezing of hard ellipsoids, and find that the description of the structure of crystalline phases is improved in comparison to the commonly used second-order theory. For the case of orientational freezing, it is found that the higher-order contributions do not modify the predictions of the second-order theory, and that accurate liquid structure appears to be the key factor leading to improved description of the nematic phase