A unified formalism is presented, which is applicable to a wide class of problems related to fast-neutron multiplying systems. Such problems are the search for asymptotic and transient space-energy modes in fast reactors and exponential or wave experiments and the analysis of pulsed or modulated bare systems. This formulation is based on the use of a Laplace transformation with respect to time and of a Fourier transformation with respect to space. It is greatly simplified, if it is assumed that the fission spectrum is independent of the energy of the incident neutron and of the nuclide that underwent fission. This assumption, which does not affect the results appreciably, makes it possible to describe the whole neutronic process in terms of a single scalar variable, the fission neutron source, (instead of the energy-dependent flux) without any loss of information. Furthermore, the solution can be found by convolutions over the neutronic processes between successive generations of fissions, which involve only simple slowing-down kernels.