Space-dependent reactor kinetics problems can be solved by response techniques in which subassemblies of the core (called cells) are treated as “black box” transducers of neutron currents. In this paper we present a continuous integral theory of space-time neutronics, reduce this theory to an approximate response-matrix method, and solve some monoenergetic one-dimensional problems.The principal advantage over more usual reactor kinetics methods is the achievement of accuracy with a coarse spatial grid. Previously, criticality calculations using response-matrix methods had established this principle. The present work extends the result to time-dependent situations.The author believes that development of the response-matrix technique can significantly reduce the computational effort required for solution, without loss of accuracy, of a broad class of space-time reactor problems.