In its lowest-energy three-dimensional (3D) hexagonal crystal structure (γ phase), In2Se3 has a direct band gap of ∼1.8 eV and displays high absorption coefficient, making it a promising semiconductor material for optoelectronics. Incorporation of Te allows for tuning the band gap, adding flexibility to device design and extending the application range. Here we report results of hybrid density functional theory calculations to assess the electronic and optical properties of γ-In2Se3, γ-In2Te3, and γ-In2(Se1-xTex)3 alloys, and initial experiments on the growth and characterization of γ-In2Se3 thin films. The predicted band gap of 1.84 eV for γ-In2Se3 is in good agreement with the absorption onset derived from transmission and reflection spectra of thin films. We show that incorporation of Te gives γ-In2(Se1-xTex)3 alloys with a band gap ranging from 1.84 eV down to 1.23 eV, thus covering the optimal band gap range for single-junction solar cells. In addition, the γ-In2Se3/γ-In2(Se1-xTex)3 bilayer could be employed in tandem solar-cell architectures absorbing at Eg ≈ 1.8 eV and at Eg ≤ 1.4 eV, toward overcoming the ∼33% efficiency set by the Shockley-Queisser limit for single junction solar cells. We also discuss band gap bowing and mixing enthalpies, aiming at adding γ-In2Se3, γ-In2Te3, and γ-In2(Se1-xTex)3 alloys to the available toolbox of materials for solar cells and other optoelectronic applications.