The kinetic theory of heterogeneous nucleation of a liquid developed by Nowakowski and Ruckenstein [J. Phys. Chem. 96 (1992) 2313] for a planar surface is extended to the nucleation of liquid clusters in spherical nanocavities of a solid surface. It is shown that for all considered contact angles and radii of the cavity, the nucleation rate is higher than that on a planar surface and that it increases with increasing strength of the fluid-solid interactions. The difference is small at high supersaturations (small critical clusters), but is orders of magnitude higher at lower supersaturations when the cluster has a size comparable with the size of the cavity. At constant contact angle the nucleation rate increases with increasing curvature of the cavity. The dependence of the nucleation rate on the contact angle is not monotonous. (C) 2010 Elsevier Inc. All rights reserved.