The lowest excited states of nuclei with spherical ground states are vibrational collective states at excitation energies of a few MeV, described by the RPA picture as coherent oscillations of the nuclear shape. Deformed nuclei also have vibrational states, with energies comparable to those of spherical nuclei with nearby masses. But the vibrational states of deformed nuclei are never their lowest excited states. Instead, each deformed nucleus has a set of excited states with energies much less than 1 MeV. These low-lying states appear to be collective: like the vibrations, they are strongly excited by the Coulomb fields of passing projectiles. Their energies, too, vary smoothly with the masses of the deformed nuclei; in fact, they are even more regular than the vibrational energies, with groups of states of various angular momenta occuring in typical patterns of excitation energies. The characteristic rotational spectrum is only a good approximation when the mean field ground state is strongly anisotropic.