The ignition of reactive materials by a shock wave, when the chemistry is governed by chain-branching kinetics, is investigated using a combination of high activation temperature asymptotics and numerical simulations. A two-step chemical model is used. The first step is a thermally neutral induction time, representing chain initiation and chain branching, which has a temperature-sensitive Arrhenius form of the reaction rate. At the end of the induction time is a transition point where the fuel is instantaneously converted into chain radicals. The second step is a temperature-insensitive exothermic reaction, representing chain recombination. It is found that the initiation process is qualitatively different from that for a temperature-sensitive one-step reaction considered previously. Three different cases, when the rate of heat release is slow, comparable and fast compared to the initial induction time, are considered. In each case ignition first occurs at the piston and the transition point (which marks the end of the induction zone and the start of the main heat release zone) initially propagates away from the piston at subsonic speeds, so that pressure and temperature disturbances from the exothermic region overtake the transition path and accelerate it. For rapid rates of heat release, a secondary shock is very promptly formed near the piston, which is subsequently amplified into a strong detonation propagating through the induction zone behind the leading shock. However, unlike for one-step kinetics the formation of the secondary shock does not involve quasisteady weak detonations. For moderate rates of heat release a secondary shock still eventually forms at the front of the disturbed region of the induction zone behind the leading shock, but a detonation is not formed until after the collision of the shocks. When the rate of heat release is slow, the transition point is continuously accelerated, but its speed remains subsonic until disturbances due to the heat release overtake the shock. No secondary shock forms for this case, completely unlike the case for one-step kinetics. (C) 2002 American Institute of Physics.