The rotatory-thermal instability of a couple-stress fluid heated from below is investigated. Following the linearized perturbation stability theory and normal mode analysis, the paper mathematically established the condition for the onset of oscillatory motions which may be neutral or unstable for rigid boundaries at the top and bottom of the fluid. It is established that all non-decaying slow motions starting from rest, in a couple-stress fluid of infinite horizontal extension and finite vertical depth, which is acted upon by uniform vertical rotation opposite to gravity and a constant vertical adverse temperature gradient, are necessarily oscillatory, if 4 8 2 1 F TA , where A T is the Taylor number and F is the couple-stress parameter, the result is also in accordance with corresponding configuration of Newtonian fluid when the couple-stress parameter F=0, by Gupta etal 1 .__ampersandsignnbsp;