The effect of an electric field on the overall intensity of the ZEKE spectrum and on the lifetime is discussed for very long living states detected by a pulsed field ionization delayed by several microseconds or more. It is shown that the presence of a de electrical field can shorten the very long lifetimes and that it can also reduce the overall intensity of the very long living states, The decrease in the long lifetimes of the ZEKE states is complementary to the field-induced elongation of the shorter lifetimes. The discussion is based on quantum mechanical considerations and is illustrated by detailed computational studies, for a model problem, using an effective Hamiltonian formalism for an energy range just above the lowest ionization threshold, The model allows for coupling of different Rydberg series built on different excited states of the core where the continuum corresponds to the ground state. Predissociation is not allowed for in the model Hamiltonian. The trends are in accord with the observations of Held et al, as reported in the preceding paper, and the magnitude of the measured lifetimes of the ZEKE states (dozens of microseconds) are reproduced by the computations.