The process of synthesis of nanofibrous carbon from methane achieved in an isothermal plug flow reactor with a fixed bed of catalyst 90 wt.% Ni-Al2O3 is considered. It is shown that the equations allow a solution in the form of a progressive wave of deactivation that moves at a constant rate and has a stationary profile. Analytic dependencies are obtained to calculate the wave rate and carbon content in the deactivated catalyst. The process parameters are calculated at 823 K and specific methane consumption 120 l/h g. The process parameters are compared for two types of reactors operating at identical conditions: a plug flow reactor with the fixed catalyst bed and a reactor with perfect mixing of catalyst particles and gas. The specific carbon yield is shown to be higher in the latter. (c) 2006 Elsevier B.V. All rights reserved.