A molecular theory is presented of new differential light-scattering effects in a fluid, whose existence has been qualitatively predicted by recent symmetry-based arguments. These new effects, both natural and field-induced, differ from the known circular intensity differentials in the use, first, of additional polarization states for the incident beam and for the analysis of the scattered light and, secondly, of different directions of any applied field. To explain all the new intensity differentials the present theory has had to extend existing ones by including the contributions to the scattered radiation of the electric octopole and magnetic quadrupole induced in a molecule. Many of the new differentials are too small to be measured currently and only those of magnitude comparable with existing effects are presented. Some of these are independent of the various known circular intensity differentials and include an effect which provides a means in principle for measuring the high-frequency magnetizability of an atom.