The thermal stability of two dimensional parallel convective motion in a fluid confined between two vertical cylinders is studied. The convective motion is induced by nonuniformly distributed heat sources in the fluid layer. A spectral collocation method is employed to solve the axisymmetric perturbed equations arising in the linear stability analysis. The stability boundary depends on the source distribution parameter, source strength parameter, Prandtl number and radius ratio. In general the flow remains least stable when the source distribution parameter is maximum in the middle of the two bounding cylinders. Thermal buoyancy mode of instability is introduced by the source distribution parameter for lower values of the radius ratio. (c) 2005 Elsevier Ltd. All rights reserved.