viscoelastic fluid behaves like a Newtonianfluid. It is found that rotation has a stabilizing effect, whereas the magnetic fieldhas both stabilizing and destabilizing effects. Graphs have been plotted by givingnumerical values to the parameters, depicting the stability characteristics. The ro-tation, magnetic field, and viscoelasticity are found to introduce oscillatory modesin the system that were nonexistent in their absence.* * *IntroductionA comprehensive account of thermal convection in a fluid layer under varying assumptions ofhydrodynamics has been summarized in the celebrated monograph by Chandrasekhar [1]. Bhatiaand Steiner [2] have studied the thermal instability of a Maxwell fluid in the presence of rotation andhave found that the rotation has a destabilizing influence, for a certain numerical range, in contrastto the stabilizing effect on Newtonian fluid. Eltayeb [3] considered the convective instability in arapidly rotating Oldroyd fluid (i.e., fluid described by the Oldroyd [4] constitutive relations). Bhatiaand Steiner [5] have also studied the problem of thermal instability of a Maxwell fluid in hydromag-netics and have found that the magnetic field has the stabilizing influence on viscoelastic (Maxwell)fluids just as in the case of Newtonian fluid. Sharma [6] has studied the thermal instability of a layerof Oldroyd fluid acted on by a uniform rotation and found that the rotation has a destabilizing aswell as stabilizing effect under certain conditions, in contrast to the Maxwell (viscoelastic) fluid,where it has destabilizing effect [2].There are many viscoelastic fluids that cannot be characterized by Maxwell’s constitutive rela-tions or Oldroyd’s constitutive relations. One such class of viscoelastic fluid is Walters