A nonlinear model of coupled diffusion and nth-order chemical reaction in a spherical catalyst pellet is revisited in this paper. As we are aware, except for the linear case n = 1, no exact solutions of this model have been reported until now. In the present paper several such solutions are given in a closed analytical form. The existence and uniqueness of solutions in the whole range n >= 0 of the reaction order and of the Thiele modulus phi is discussed in some detail. (C) 2010 Elsevier B.V. All rights reserved.