Variational method for investigation oscillation of temperature and synthesis gas concentration inside spherical catalytic particle is developed. Approximate distributions of temperature and concentrations in a particle with internal heat release and synthesis gas consumption are obtained. Stationary parameters are found on the base of equations for square of norms functions which present temperature and concentrations distributions. In the frame of small disturbances of temperature and concentrations thermal stability is investigated. Variational principle is used for estimation first eigenvalues of system of partial differential equations with essentially variable coefficients. It is revealed, that diffusion resistance of synthesis gas inside a porous particle can lead to occurrence oscillation regime. Approximated results are compared with direct numerical experiments for modeling nonstationary heat and mass transfer in a catalytic porous particle. Two approaches for describing heat and mass stability of catalytic particle with internal heat source and synthesis gas loss are discussed. (C) 2009 Elsevier Ltd. All rights reserved.