The large time behavior of the lifetime distributions of active intermediates is investigated for nonequilibrium chemical systems with stable limit cycles. The lifetime distributions are the solutions of a system of partial differential equations which can be integrated by using the method of characteristics. A generalized H-function is defined in terms of two sets of solutions of these partial differential equations corresponding to two different initial solutions. An H-theorem is proven which shows that for a system with a stable limit cycle ail transient lifetime distributions evolve toward the same normal form which is a periodic function of time and which, up to a constant phase factor, is independent of the initial conditions. A frequency response tracer experiment is suggested for the evaluation of the probability distribution of the lifetime of an intermediate. A special experiment makes possible the direct measurement of the Fourier transform of the probability distribution with respect to the lifetime of a molecule. This Fourier transform. is a generalized susceptibility function which depends both on time and frequency. The real and imaginary parts for the susceptibility function are related to each other by means of a set of generalized Kramers-Kronig relationships, which are a consequence of causality. The theory is used for generalizing the kinetic spectrum analysis of time-dependent normal processes. An alternative approach to spectral kinetic analysis determines the influence of environmental fluctuations on the lifetime distributions. It is shown that the average lifetimes of active intermediates in the system increase with the strength of environmental fluctuations and in the limit of random processes with long memory, even though the concentrations remain finite, the average lifetimes tend to infinity. A numerical computation of the large time behavior of active intermediates is carried out in the particular case of the Selkov model with a stable limit cycle. The numerical analysis confirms the theoretical predictions presented in the article.