Electron and hole trapping in substoichiometric germanium oxides are investigated through the use of hybrid density functionals. We consider disordered model structures generated by Monte-Carlo bond switching and by ab initio molecular dynamics (MD). The Monte-Carlo model consists of fourfold coordinated Ge atoms and of twofold coordinated O atoms, and does not show trap levels neither for electron nor for holes. At variance, the MD model shows threefold coordinated O and Ge atoms forming valence alternation pairs and is found to present trap states for both carriers. The trapping states correspond to the formation and breaking of Ge-Ge bonds. The associated defect levels are determined within a band diagram of the Ge/GeO"2 interface.