The structural and evolutionary conditions which allow high mass stars (M > 4 M ) to become Cepheid variables are examined. The important internal parameters for determining the location of stars in H-R diagram are isolated from computed sequences of static models. It is demonstrated that the existence of a (reasonably long lived) Cepheid phase depends largely on the composition profile near the shell source. The interplay of the various processes which take place during actual evolution is concisely expressed in a semi-empirical relation between effective temperature and core mass (or helium content in the core) for the static situation. A qualitative interpretation of the computed results is offered. For ` extreme' Population I composition only stars with 4 < MIM5 7 can spend a substantial time within the Cepheid instability region in the H-R diagram during post red giant evolution. In the higher mass range, stars cross the Cepheid region very rapidly as a result of a secular instability which arises when a critical ratio between core and shell source luminosity is exceeded in the giant region. The existence of two branches of chemically identical solutions of the stellar structure equations-one stable, the other demonstrated.