What causes the expansion and contraction of Cepheids?

In ordinary stars, hydrostatic equllibrium diminishes these pulsations. Basically, Starr's in this stage can create conditions that trap their radiated energy in the outer layers. The pressure increases enough so that the outer layers expand.

Why do Cepheid stars pulsate?

A Cepheid pulsates in a regular and predictable cycle. It is thought that Helium is involved in its cycle. Doubly ionized Helium is more opaque than singly ionized helium, meaning it lets little light through. At the dimmest part of the cycle, doubly ionized Helium makes up the outer layers of the star.