We consider a model for collective dynamics where particles move at a constant speed and change their direction of motion to align with the direction of motion of their neighbours, up to some noise. In particular, particles may align in the same or opposite orientation; this is called nematic alignment. Starting from this particle model we derive a macroscopic model for the particle density and mean direction of motion which corresponds to a cross-diffusion system. The derivation is carried over by means of a Hilbert expansion. This cross diffusion system poses many new challenging questions. This is a joint work with Pierre Degond (Imperial College London, UK).