Detailed theoretical investigations of stellar pulsation need a mass and a composition before models can be constructed for study. Unfortunately, for the last ten years the masses of the Cepheids, which can be determined with reasonable accuracy by six different methods, have been in dispute. One possible way to resolve these various mass anomalies is to postulate an inhomogeneous composition envelope structure. Thus the principal problem in current theoretical studies is: What are both the masses and envelope compositions of Cepheids?

Stellar evolution theory has indicated that main sequence B stars evolve to become red giants or supergiants and then loop blueward in the Hertzsprung-Russell diagram to cross again the pulsation instability strip the second and third (or even more) times. The second and third crossings are the slowest for models of evolutionary masses between 4 and 13 M⊙. Both below and above this mass the stars become Cepheids (or δ Scuti variables at the lowest masses) on their sole crossing to the red. Massive stars do not become cool enough to become Cepheids if the main sequence mass is above 18 M⊙.