In this paper, the growth of orthorhombic and monoclinic (AlxGa1-x)(2)O-3 thin films on (00.1) Al2O3 by tin-assisted pulsed laser deposition is investigated as a function of oxygen pressure p(O-2) and substrate temperature T-g. For certain growth conditions, defined by T-g >= 580 degrees C and p(O-2) <= 0.016 mbar, the orthorhombic kappa-polymorph is stabilized. For T-g = 540 degrees C and p(O-2) <= 0.016 mbar, the kappa-, and the beta-, as well as the spinel gamma-polymorph coexist, as illustrated by XRD 2 theta-omega-scans. Further employed growth parameters result in thin films with a monoclinic beta-gallia structure. For all polymorphs, p(O-2) and T-g affect the formation and desorption of volatile suboxides, and thereby the growth rate and the cation composition. For example, low oxygen pressures lead to low growth rates and enhanced Al incorporation. This facilitates the structural engineering of polymorphic, ternary (Al,Ga)(2)O-3 via selection of the relevant process parameters. Transmission electron microscopy (TEM) studies of a kappa- (Al0.13Ga0.87)(2)O-3 thin film reveal a more complex picture compared to that derived from x-ray diffraction measurements. Furthermore, this study presents the possibility of controlling the phase formation, as well as the Al-content, of thin films based on the choice of their growth conditions.