The properties of adiabatic non-radial oscillations of spherical stars are analysed, both analytically and numerically. A strict upper bound on the frequencies of g+ modes is found, related to the local buoyancy and acoustic frequencies. By analysing asymptotically the low order modes with high l these are shown to be split into modes trapped near the surface and modes trapped at the local maxima of the buoyancy frequency and asymptotic expressions for the frequencies of the modes in these groups are derived. At points where their frequencies agree, modes from two different groups exhibit avoided crossings, and the nature of one of these is analysed in detail.