A study is made of Raman light scattering on magnons in a many-sublattice antiferromagnet in a magnetic field parallel to the easy axis. An investigation method is developed which makes possible the optimum use of the magnetic symmetry. As an example, the scattering in a four-sublattice rhombic antiferromagnet at T=0 for all realised magnetically ordered phases is investigated. The form of the scattering tensor is obtained and the dependence of its components on the magnetic field is calculated. Emphasis is given to the study of light scattering on exchange modes. The contribution of the exchange mechanism to the single-magnon scattering tensor is discussed.