The problem of optimal activity distribution in an nonisothermal catalyst pellet with a consecutive-parallel reaction scheme proceeding in a created nonsteady state conditions already studied in our previous paper [1], is now extended to the case where the temperature and the concentrations of the reactants inside the grain vary according to time. The same activity distribution, i.e., a Dirac delta function, as in the case of quasi-steady state, is also found optimal in this case. The studied perturbed system gives better catalytic performances for large periods compared to time characteristic of the catalytic process. (C) 2010 Elsevier B.V. All rights reserved.