Catalytic ignition and extinction processes are analyzed in this paper. The premixed fuel flows towards a catalytic plate of finite thermal conductivity and thickness. The effect of the external heating or cooling on these critical phenomena is also evaluated. Depending on the ratio of the thermal resistance of the plate to the gas, the transition to the weakly reactive to the strong reactive flow can be single or multivalued, for a high activation energy of the catalytic reaction. Analytical expressions for the critical Damkohler numbers for ignition and extinction are obtained. Also, transient processes leading to catalytic ignition are studied and ignition times for a catalytic adiabatic plate are obtained.