We have synthesized members of an isostructural solid solution series KxBa1-xO2-delta (x <0.41, delta <0.11) containing mixed-valent dioxygen anions. Synthesis in liquid ammonia solution allows a continuous range of compounds to be prepared. X-ray and neutron diffraction show that KxBa1-xO2-delta adopts the tetragonal rocksalt-derived structure of the end members KO2 and BaO2, without any structural phase transition down to 5 K, the lowest temperature studied here. We identify four oxygen-oxygen stretching modes above 750 cm(-1) in the measured Raman spectra, unlike the spectra of KO2 and BaO2 which both contain just a single mode. We use density functional theory calculations to show that the stretching modes in KxBa1-xO2-delta arise from in-phase and anti-phase coupling of the stretching of nearest-neighbor oxygen dimers when the valence state of the dimers lies between -1 and -2 because of mixed cation coordination. This coupling is a direct signature of a novel type of anionogenic mixed valency.