Starting from the equations of modified gravity hydrodynamics, we derive the equ tions of motion governing linear, adiabatic, radial perturbations of stars in scalar-tensor theories. There are two new features: first, the eigenvalue equation for the period of stellar oscillations is modified such that the eigenfrequencies are always larger than predicted by General Relativity. Second, the General Relativity condition for stellar instability is altered so that the adiabatic index can fall below 4/3 before unstable modes appear. Stars are more stable in modified gravity theories. Specialising to the case of chameleon-like theories, we investigate these effects numerically using both polytropic Lane-Emden stars and models coming from modified gravity stellar structure simulations. The change in the oscillation period can be as large as 50% and the critical adiabatic index for instability falls by a composition dependent amount of order 10^(-1). By solving the new equation for Cepheid models, it is found that the change in the inferred distance using the period-luminosity relation can be up to three times larger than if one had only considered the modified equilibrium structure. We discuss the implications of these results for recent and up-coming astrophysical tests and estimate that previous methods can produce new constraints such that the modifications are screened in regions of Newtonian potential of order 10^(-8).

Version 3: Updated to reflect published version. Mainly typos but the discussion of certain approximations has been expanded. Results and content unchanged from previous versions