The alloying of the transparent semiconducting sesquioxides In2O3 and Ga2O3 can lead to a modulation of the parent compound properties, e.g., the shallow-/deep-donor character of the oxygen vacancy or the presence/absence of a surface electron accumulation layer. In this work, we investigate the effect of alloying on the electron transport properties of unintentionally-doped single-crystalline and textured bixbyite (In1-x
Ga
x
)2O3 thin films annealed in oxygen and vacuum with Ga contents up to x=0.18. Hall effect measurements demonstrate a surprising increase in electron density with added Ga, potentially related to the incorporation of Ga-interstitials or oxygen vacancies induced by unit-cell distortions. Investigations based on x-ray photoelectron spectroscopy measurements demonstrate the existence of the surface electron accumulation layer for all alloy films and, hence, no depletion up to x=0.18. Additionally, we demonstrate a single-crystalline (In0.92Ga0.08)2O3:Sn film, as a possible transparent conductive oxide with a wider band gap than that of Sn-doped In2O3.