We report the results of a molecular dynamics computer simulation of particles interacting via the Gay-Berne potential with parameters selected to approximate those of mesogenic molecules. The system was found to form a variety of mesophases as the temperature was lowered. We have characterized these phases with the aid of computer graphics techniques to visualize the molecular organization within configurations taken from the production stage of the simulations. The phases have been identified, on the basis of such images, as isotropic, nematic, smectic A, smectic B and crystal. © 1990 Taylor & Francis Group, LLC.