A simple model is developed to describe the time-dependent neutron spectrum in pulsed systems whose decay may be dominated by either a fundamental or a pseudofundamental mode. Such systems include a large class of fast multiplying assemblies and thermal nonmultiplying assemblies. The simple model provides qualitative understanding of the role played by the fundamental or pseudofundamental mode in the kinetic evolution of the time-dependent neutron flux and, when optimized by a variational principle, gives excellent quantitative descriptions of the flux for a wide range of systems. Trial functions are presented which, when adjusted with a suitable variational principle, provide a good estimate of the shape and decay rate of the dominant reproducing mode of such systems. The method works well for systems where a fundamental mode exists and is also applicable in the range where pseudofundamental mode behavior is observed. Eigenfunction eigenvalue solutions are obtained for the fast multiplying system GODIVA and these, together with similar solutions for beryllium, provide a basis of comparison for the variational methods. The investigation shows that care should be exercised in associating reactivity and period parameters with far subcritical systems because the flux shape is changing substantially and the major regenerative mode is not isolated when the eigenvalue associated with this mode lies in the continuum. In the farther subcritical region an example shows a complete lack of a single dominant mode.