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Many of the observed features in the period histogram of CVs and LMXBs can be theoretically explained. However, there still exists much debate over many details of compact binary evolution. The apparent shortage of progenitor systems for low-mass binary pulsars, the scarcity of short period LMXBs, as well as the origin and evolution of evaporating binary pulsars are of great concern. In light of this controversy, we have developed a simple numerical integration routine to follow the secular evolution of compact binaries. Due to the uncertainties in the physics, i.e. the exact form of magnetic braking law, the effects of evaporation, etc, many evolutions need to be explored. A full stellar code hides much of the basic physics, while it introduces parameters that further complicate the matter. Excessive computational time, the primary disadvantage in a full stellar code, severely restricts the parameter space which can be explored. There seems to be an inherent need for an inexpensive technique which can be used to do explorative studies. We are able to construct evolutional scenarios for CVs and LMXBs with very little computational expense. In particular, we have developed possible evolutionary tracks for evaporating pulsars PSR 1957+20, PSR 1718+19, 47 Tuc and Ter 5A. Our scheme assumes that an equilibrium mass-radius relationship exists for the secondary star and that its radius changes due to mass loss and thermal relaxation. Although the technique is not as sophisticated as other evolutionary methods, its simplicity provides a clear insight into the underlying physics. The method also allows exploration of a variety of different input parameters. The program can direct us to the physical parameters which have significant effects and to parts of the evolution that should be studied in more detail. We are able to incorporate X-ray irradiation and get stable mass transfer rates of $10^{-8}{\rm M} \sb\odot$/yr which last only a small portion of the binary evolution. During the rest of the evolution, the binary is either visible as an evaporating pulsar or invisible. This wor
k is supported in part through NSF grant AST-9020855 and NASA grant NAGW-2447.
