The structures in amorphous (a-) Zn, Sn co-doped In2O3 (ZITO) thin films grown by pulsed laser deposition on glass under varying oxygen pressure or with varying Sn:Zn ratios were determined using X-ray absorption spectroscopy and anomalous X-ray scattering. Typical structures around cations in a-ZITO films are described and compared with crystalline (c-) ZITO films. The results show that the Zn cations are fourfold coordinated with Zn-O bond lengths of 1.98 +/- 0.02 angstrom, which is close to that in bulk ZnO. As a consequence, the second coordination shells around Zn contract. At longer distances away from Zn, the structure is commensurate with the averaged structure. The unit volume around In also contracts slightly compared to bulk In2O3, whereas the Sn-O bond length is similar to the one in bulk SnO2. These unique structural characteristics may account for the films' superior thermal stability over amorphous Sn-doped In2O3, and suggest that Zn and Sn act as network-forming cations. Like in c-ZITO, coordination numbers (N) around Sn, In, and Zn follow the order N-Sn > N-In > N-Zn. Unlike in c-ZITO, where electrical properties change significantly with a slight variation in the Sn:Zn ratio, this variation does not markedly alter the electrical properties, or the local structures, of a-ZITO films. Dramatic changes in the electrical properties occur for films grown under various oxygen pressures, which point to oxygen defects as the source of charge carriers.