Abstract : The structure of a very strong shock wave propagating through a deuterium-tritium gas mixture and a pure tritium gas is studied. The temperature behind the shock wave is sufficiently high so that thermonuclear reaction probabilities are large. The wave structure is similar to that of detonations in chemically reacting gases. It is assumed that the characteristic times for collisions and reactions are such that the von Neumann-Zeldovich model of detonations is applicable; i.e., the shock can be treated as a viscous gas dynamic shock followed by a deflagration wave inside of which all the reactions occur. The physical and mathematical assumptions involved in the analysis of thermonuclear shock wave structure are examined. The reaction probabilities for deuterium and tritium fusion reactions are computed and the appropriate reaction kinetics equations are developed. The effect of energy losses due to bremsstrahlung on the wave structure is considered for a gas that is optically thin to radiation of all frequencies. The resulting set of structure equations are solved numerically for several physically interesting cases. The neutron flux and power output due to reactions is calculated for a shock propagating in a electromagnetically driven shock tube filled with a mixture of deuterium and tritium. A power of 1 kw/per cubic centimeter is predicted under specified operating conditions.