We discuss the theory and phenomenology of the interplay between the massless graviton and its massive Kaluza-Klein modes in the Randall-Sundrum two-brane model. The equations of motion of the transverse traceless degrees of freedom are derived by means of a Green function approach as well as from an effective nonlocal action. The second procedure clarifies the extraction of the particle content from the nonlocal action and the issue of its diagonalization. The situation discussed is generic for the treatment of two-brane models if the on-brane fields are used as the dynamical degrees of freedom. The mixing of the effective graviton modes of the localized action can be interpreted as radion-induced gravitational-wave oscillations, a classical analogy to meson and neutrino oscillations. We show that these oscillations arising in M-theory-motivated braneworld setups could lead to effects detectable by gravitational-wave interferometers. The implications of this effect for models with ultra-light gravitons are discussed.