The short range order in Ge30Ga5Sb10Se55 and Ge21Ga5Sb10Se64 glasses was investigated by X-ray (XRD) and neutron diffraction (ND) as well as extended X-ray absorption fine structure (EXAFS) measurements at the Ge, Ga, Sb and Se K-edges. Large scale structural models were obtained by fitting simultaneously the experimental data sets by reverse Monte Carlo (RMC) simulation technique. It was found that Ge, Sb and Se atoms follow the Mott-rule and have 4, 3 and 2 nearest neighbors, respectively. The average coordination number of the Ga atoms was around 4. The structure of these glasses can be described by the chemically ordered network model: the Ge–Se, Ga–Se and Sb–Se bonds are the most prominent while Ge–Ge and Ge–Sb bonds are formed only in Se-poor compositions. Models generated by RMC contained some long distances (0.3–0.4 Å higher than the usual covalent bond lengths) between Ge–Se and/or Ge–Ge pairs. Dedicated simulation runs confirm the existence of these bonds. •Structural models of GeGaSbSe glasses consistent with multiple datasets are created.•These glasses can be described by the chemically ordered network model.•Ge, Sb, Se and Ga atoms have 4, 3, 2 and 4 nearest neighbors, respectively.•Ge-Ge (or Ge–Ga) bonds can be found in both Se deficient glasses.•In Ge30Ga5Sb10Se55 glass Ge–Sb bonds also exist.