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In this paper we report methods of computation which have been developed to provide a theoretical understanding of the RR Lyrae and Cepheid type pulsating stars. The results reported are intended to illuminate the methods of calculation and to provide insight into the physical processes in these stars. A survey of pulsation in RR Lyrae models using these methods has also been carried out and will be reported soon in another journal. A survey of pulsation in Cepheid models has been initiated and will be continued.

Nonlinear calculation methods for model representing W virginis, noting rapid amplitude growth and luminosity-to-mass ratio

Computation method used in pulsation of Lyrae models extended to models of Cepheid variables, noting instability of appropriate period, mass size, luminosity and velocity curves

The relation of the hydrogen ionization zone to stellar pulsation is discussed. A detailed analysis of the behavior of this zone in SU Draconis, shows that it is an important energy source for driving pulsation. An examination of conditions in other RR Lyrae stars, cepheids, and W Virginis stars suggests that the hydrogen ionization zone is important in determining the phase lag and in driving their oscillation. It is proposed that non-spherical pulsationtype motions, driven by the hydrogen ionization instability, are present in all the late-type giants and supergiants and provide the principnl means of energy transport in the hydrogen ionization zone of such stars. These motions could account for indications of variability and supersonic velocities in their photospheres. Numerical calculations have been initiated to develop these ideas further. It is also shown that the dissociation transition of molecular hydrogen may provide the heat sink that is the key to the existence of the class of cool variables that include the Mira and semiregular red variables. (auth)