A new method is presented for investigating the behavior of pulsed fast neutrons in non-multiplying semi-infinite systems. The time- and space-dependent multigroup P1 equation (of the telegrapher’s equation type) was analytically solved by the use of the Laplace transform. Starting from the space dependent first time moments on the decaying group-wise neutron fluxes, the propagation parameters are newly defined as the fundamental parameters to describe the characteristics of the fast neutron moderation in the medium. These parameters include the space independent mean life time and the inverse of the effective velocity of neutron propagation. The proposed method will be useful in investigating the space dependent neutron slowing down and propagation phenomena in assemblies.