The model for coupled diffusion and nt(h)-order reaction in a spherical catalyst pellet, which is a strong nonlinear differential equation with boundary values, is solved using the Adomian decomposition method. The explicit solutions for concentration profiles and effectiveness factors, for the model equation, are obtained and compared with the solutions obtained by a finite difference numerical method. For reaction orders less than 1.0, the Adomian polynomial series solution with 4 terms gives comparable results to those obtained with a finite difference numerical procedure. For reaction orders greater than 1.0, series solutions with more than 6 terms, are required for good accuracy.