The atmospherically important species O-2(a (1)Delta(g)) has been studied by photoelectron spectroscopy using vacuum ultraviolet radiation from a synchrotron as the photon source. Constant-ionic-state (CIS) spectra, recorded for vibrational levels of O-2(+)(X (IIg)-I-2,) nu(+)=0,1,2,3 accessed from O-2(a (1)Delta(g)) nu "=0, exhibit intense signals in the photon energy region 14.0-15.5 eV which are shown to arise from autoionization from a Rydberg state with an O-2(+)(C (2)Phi(u)) core. On the basis of the results obtained and earlier evidence derived from vacuum ultraviolet absorption spectroscopy, this state is assigned as a (C (2)Phi(u), 3s sigma(g)) (1)Phi(u) Rydberg state. Photoelectron spectra recorded for O-2(a (1)Delta(g)) at positions of strong resonances have allowed extended vibrational structure to be obtained in the first photoelectron band. The relative vibrational component intensities in the resonant photoelectron spectra are in good agreement with computed relative intensities obtained via Franck-Condon calculations, confirming the vibrational numbering of the resonances in the (1)Phi(u) state. Competition between autoionization and predissociation in the (1)Phi(u) Rydberg state is discussed on the basis of the results obtained. Weaker structure is observed in CIS spectra recorded in the photon energy regions 12.5-13.5 and 15.0-20.0 eV. Suggestions are made for the nature of the highly excited states of O-2 associated with this structure, based on available ionization energies and spectroscopic constants of known ionic states accessible from O-2(a (1)Delta(g)). For example, two broad bands centered at approximate to 16.4 and approximate to 17.75 eV are assigned to excitation to Rydberg states arising from the configurations (D (2)Delta(g), 3p pi(u)) and (D (2)Delta(g), 4p pi(u)) respectively.