Epitaxial films of mixed Ce1-xZrxO2(001) oxides with x less than or equal to 0.3 have been grown on SrTiO3(001) by oxygen-plasma-assisted molecular beam epitaxy. The film growth at 600 degrees C is predominantly nucleation and growth of three-dimensional islands. The films become much smoother after rapid thermal annealing at 700 degrees C for 30 s in the oxygen plasma. High-energy ion channeling reveals that Zr atoms substitutionally incorporate at cation sites in the CeO2 lattice for all doping levels, leading to Ce1-xZrxO2 solid solutions. Analysis of Zr 3d and Ce 3d core-level binding energies shows that the oxidation state of both Zr and Ce is +4. Lattice distortion induced by incorporation of Zr in the CeO2 lattice becomes prevalent for high doping levels and surface roughen accordingly.