We have proposed recently to extend the use of the Dissipative Particle Dynamics (DPD) technique to the study of anisotropic mesophases, following its proven effectiveness in describing isotropic complex fluids. This technique circumvents, at least in part, the serious limitations on time-scales and physical dimensions inherent to molecular modelling simulations, e.g. Molecular Dynamics (MD) and Monte Carlo (MC) techniques. In this work some preliminary results for systems made up of single mesogenic units are presented, including examples of formation of nematic phases. The reorientation process of mesogenic DPD chains under the influence of an external field and of shearing stresses are explored as illustrative cases. Once the methodology for generating mesogenic units is well implemented it will be possible to use these units as building blocks for more complex structures like polymer liquid crystals or liquid crystalline suspensions of short fibers in a polymeric matrix.