Effect of Hall currents is considered on Walters' (Model B') elastico-viscous fluid heated and soluted from below in the presence of a vertical magnetic field. A dispersion relation governing the effects of viscoelasticity, salinity gradient, rotation, magnetic field, and Hall current is derived. For the case of stationary convection, the Walters' (Model B') fluid behaves like an ordinary Newtonian fluid. The compressibility, stable solute gradient, rotation, and magnetic field postpone the onset of thermosolutal instability, whereas Hall currents are found to hasten the onset of thermosolutal instability in the absence of rotation. In the presence of rotation, Hall currents postpone/hasten the onset of instability depending upon the value of wave numbers as small/large. Again, the dispersion relation is analyzed numerically and the results depicted graphically. The viscoelasticity, solute gradient, and magnetic field (and corresponding Hall currents) introduce oscillatory modes in the system that were nonexistent in their absence. The case of over-stability is discussed and sufficient conditions for nonexistence of over-stability are derived.