Summary.An analysis is made of the flow generated in a semi-infinite expanse of an incompressible viscous fluid bounded by an infinite porous plate when both the fluid and the plate are in rigid-body rotation with angular velocity Ω and additionally the plate executes harmonic oscillation with frequency n in its own plane. It is found that for uniform suction at the plate, shear oscillations are confined to an oscillating Ekman layer near the plate for all values of n. Skin-friction fluctuations for the primary flow in the direction of the plate oscillations have a phase lead over the plate oscillations while their amplitude rises with Ω for a given value of n but decreases with increasing frequency for a given value of Ω. On the other hand, the skin-friction fluctuations for the transverse flow induced by the Coriolis forces have a phase lag over the plate oscillation and the amplitude of these fluctuations decreases with an increase in Ω for a given value of n. For uniform blowing at the plate, shear oscillations are confined to an oscillating Ekman layer near the plate for all values of n except n=2Ω. For n=2Ω, resonance occurs so that vorticity continues to penetrate outwards perpetually from the plate. With viscous dissipation of the kinetic energy taken into account, the corresponding exact solution of the energy equation is derived to determine the temperature distribution in the above flow under the condition of zero heat transfer between the fluid and the plate which is subject to uniform suction. It is found that the wall temperature has a mean and a second-harmonic fluctuation. For a given value of Ω, the mean wall temperature decreases with an increase in frequency provided n<2Ω but it rises with frequency for n>2Ω. For very high frequency, rotation has hardly any effect on the mean wall temperature. It is observed that for a given frequency the amplitude of the second-harmonic fluctuation decreases with an increase in Ω provided n>2Ω but it increases with rotation for n<2Ω.