The structure of (GeS2)0.75(Ga2S3)0.25 and (GeS2)0.83(Ga2S3)0.17 glasses was investigated by Raman scattering, high energy X-ray diffraction and extended X-ray absorption fine structure (EXAFS) measurements at the Ga and Ge K-edges. The reverse Monte Carlo simulation technique (RMC) was used to obtain structural models compatible with diffraction and EXAFS datasets. It was found that the coordination number of Ga is close to four. While Ge atoms have only S neighbors, Ga binds to S as well as to Ga atoms showing a violation of chemical ordering in GeS2–Ga2S3 glasses. Analysis of the corner- and edge-sharing between GeS4/2 units revealed that about 30% of germanium atoms participate in the edge-shared tetrahedra. •Structural models of GeS2–Ga2S3 glasses consistent with XRD + EXAFS data are created.•Chemical order is respected but Ga–Ga bonds are present caused by S-deficiency.•The coordination number of Ga is 3.7 ± 0.3.•The frequency and geometry of corner/edge-sharing GeS4/2 units were determined.