The phenomenon of simultaneous diffusion, reaction, and external mass transfer in a spherical catalyst particle is studied for a reaction exhibiting negative order with respect to the reactant species. With external mass transfer considered, it is shown that for a reaction exhibiting a negative order for all the concentrations, a solution to the diffusion-reaction equations does not exist for high values of Thiele modulus. An algorithm is developed to calculate the concentration profile in a spherical catalyst particle for a negative-order reaction. With the proposed algorithm, the solution is obtained even for conditions for which a solution was not found in previous studies. The algorithm successfully captures the multiplicity of the solutions as well as the transition from kinetic/intemal-diffusion controlled regime to the external mass-transfer controlled regime. The developed algorithm is further utilized to calculate the axial concentration profile in a packed-bed reactor for a negative-order reaction. Additionally, the radial concentration profile in a spherical particle is evaluated for a multi-component reaction system wherein the reaction exhibits both positive and negative order with respect to various species. The algorithm is particularly useful for power-law type negative order kinetics which are widely reported in the literature. (C) 2019 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.