Carbon deposition during catalytic CH4 decomposition (CH2 <----> C + 2H(2)), occurs at a given reaction temperature when K-M < K-M(*), where K-M(*) is the carbon formation threshold defined as the value of K-M = (P-H2(2)/P-CH4) at which the net rate of carbon deposition is zero (Snoeck et al., J. Catal. 169 (1997) 240). Carbon deposition can produce encapsulating carbon that results in catalyst deactivation, or filamentous carbon that ensures stable catalyst activity for extended periods of time. In the present study, the rate of catalyst deactivation during CH4 decomposition at 773 K on supported Co and Ni catalysts decreased as KM increased. A filamentous carbon formation threshold K-M(f) is therefore defined as the value of K-M at which the rate of catalyst deactivation equals zero as a consequence of filamentous carbon formation. Results presented herein demonstrate that stable activity and filamentous carbon formation during CH4 decomposition on supported Ni and Co catalysts can be guaranteed by choosing K-M such that the inequality K-M(f) < K-M < K-M is satisfied, whereas if K-M(f) < K-M(f) < K-M,(*) encapsulating carbon accompanied by catalyst deactivation occurs.