The study is aimed at analysing thermal convection in a compressible couple stress fluid in a porous medium in the presence of rotation and magnetic field. After linearizing the relevant equations, the perturbation equations are analysed in terms of normal modes. A dispersion relation governing the effects of rotation, magnetic field, couple stress parameter and medium permeability have been examined. For a stationary convection, the rotation postpones the onset of convection in a couple stress fluid heated from below in a porous medium in the presence of a magnetic field. Whereas, the magnetic field and couple stress postpones and hastens the onset of convection in the presence of rotation and the medium permeability hastens and postpones the onset of convection with conditions on Taylor number. Further the oscillatory modes are introduced due to the presence of rotation and the magnetic field which were non-existent in their absence, and hence the principle of exchange stands valid. The sufficient conditions for nonexistence of over stability are also obtained.
 Banyal A.S., A mathematical theorem on the onset of stationary convection in the couple-stress fluid, Journal of Applied Fluid Mechanics, 2013, Vol. 6, No. 2.
 Brakke M.K., Zone electrophoresis of dyes proteins viruses in density gradient columns of sucrose solutions, Arch. Biochem. Biophys., 1955, 55, 175.
 Chandrasekhar S., Hydrodynamic and Hydromagnetic Stability, Dover Publication, New York, 1981.
 Joseph D.D., Stability of Fluid Motions, Vol. II, Springer Verlag, Berlin 1976.
 Kumar P., Thermosolutal magneto-rotatory convection in couple stress fluid through porous medium, Journal of Applied Fluid Mechanics, 2012, Vol. 5, No. 4.
 Linden P.F., Salt and fingers in a study shear flow, Geophy. Fluid Dynamics, 1974, 6, 1.
 Nason P., Schumaker V., Halsall B., Schwedes J., Formation of a streaming convective disturbance which may occur at one gravity during preparation of samples for zone centrifugation, Biopolymers, 1969, 7, 241.
 Rana C. Gian, The onset of thermal convection in couple-stress fluid in hydromagnetics saturating a porous medium, Bulletin of the Polish Academy of Sciences, 2014, Vol. 62, No. 2.
 Rudraiah N., Chandrashekra G., Effect of couple stress on the growth rate of Rayleigh Taylor instability at the interface in a finite thickness couple stress fluids, Journal of Applied Fluid Mechanics, 2010, Vol. 3, No. 1.
 Sharma R.C., Thermal instability in compressible fluids in the presence of rotation and magnetic field, J. Math. Anal. Appl., 1977, 60, 227.
 Sharma R.C., Mehta C.B., Thermosolutal convection in compressible, rotating, couple stress fluid, Indian J. Phys., 2005, 79(2), 161.
 Sharma R.C., Sharma S., On couple-stress fluid heated from below in porous medium, Indian J. Phys., 2001, 75(2), 137.
 Sharma R.C., Thakur K.D., On couple-stress fluid heated from below in porous medium in hydromagnetics, Czech. J. Phys., 2000, 50, 753.
 Singh M., Mehta C.B., Thermosolutal convection incompressible, rotating couple stress fluid in the presence of magnetic fluid, AASRFC, 2012, 3(6), 3459.
 Singh M., Mehta C.B., On compressible couple fluid heated and sotuted from below in porous medium in presence of rotation and magnetic field, JMET, 2013, 1(1), 21.
 Spiegel E.A., Veronis G., On the Boussinesq approximation for a compressible fluid, The Astrophys. J., 1960, 131, 442.
 Stokes V.K., Couple-stresses in fluids, Phys. Fluids, 1966, 9, 1709.
 Sunil, Sharma R.C., Pal M., On a couple stress fluid heated from below in a porous medium in the presence of a magnetic field and rotation, Journal of Porous Media, USA, 2002, 149.
 Walicki E., Walicka A., Inertia effect in the squeeze film of a couple-stress fluid in biological bearings, Appl. Engng., 1999, 4.