CuxS(x;1,2) layers were grown on thermal annealing of the sequentially evaporated layer deposition (SELD) stack of Cu/S from 373 to 573 K. The thicknesses of the deposited stacks were fixed at 200 and 600 nm. The 300 K deposited layers possess a CuS (covellite) phase and a few impurity peaks of Sulphur (S). The as-deposited films of both thicknesses provided the CuS (covellite) phase with impurity peaks of Sulphur (S). The CuS single phase was observed at 373 and 473 K. The CuS transformed into a copper-rich Cu2S (chalcocite) phase at 523 K, and the same phase continued at 573 K. The Cu2S phase was obtained on re-evaporation of S from CuS at 523 K. An intermediary digenite phase was also spotted at 523 K. The CuS and Cu2S phases were confirmed from the Raman spectra. The oxidation states of Cu and S of the CuS films were also determined from XPS analysis. The Cu 2p and S 2p levels of CuS (covellite) were established using high-resolution XPS spectra. The phase transformation from CuS to Cu2S and change in stoichiometry at higher temperatures give rise to bandgap variation from 2.30 to 1.20 eV for direct and 2.10–1.34 eV for indirect allowed bandgaps. The absorption coefficient (α) for both thickness values is > 1 × 105 cm-1. Further, the 600 nm films provided higher absorption coefficient (α) values than the 200 nm layers. The unique electrical and optical properties and bandgap tuning make CuS and Cu2S thin films suitable for gas sensors, photodetectors, absorber layers in low-cost PV solar cells, and energy storage applications.