Lithium (and to some extent sodium) form simple oxides, X2O, which contain the common O2- ion.
Sodium (and to some extent potassium) form peroxides, X2O2, containing the more complicated O22- ion (discussed below).
Potassium, rubidium and caesium form superoxides, XO2. The structure of the superoxide ion, O2-, is too difficult to discuss at this level, needing a good knowledge of molecular orbital theory to make sense of it.