Structural order in the chalcogenide glasses of (As2S3)x(GeS2)1−x (x = 0.0, 0.1, 0.2, 0.4, 0.6, 0.8, 1.0) system is examined in terms of the parameters of local atomic structure as a function of composition x, obtained using high-resolution Raman spectroscopy, high-energy synchrotron X-ray diffraction, extended X-ray absorption fine structure spectroscopy and reverse Monte-Carlo modeling of diffraction data. As a result of the research carried out it is revealed that the structural order of As-rich (x > 0.4) and Ge-rich (x < 0.4) glasses is organized by the main As−S and Ge−S structural motifs based on pyramidal AsS3 and tetrahedral GeS4 units linked by =As−S−As= and Ge−S−Ge structural configurations, respectively; while for the intermediate compound with x = 0.4 the structural network seems to be better homogeneous on the nanoscale due to appearance of Ge−S−As= mixed structural configurations resulting in misbalance between corner-shared and edge-shared tetrahedral units in comparison with their predicted ratio for binary GeS2 glass and the structure of this alloy is similar to the structure of the stoichiometric glass Ge18.2As18.2S63.6 (i.e., x = 0.455) consisting of a coner-shared network of homogeneously mixed GeS4 tetrahedra and AsS3 pyramids. Based on the structural studies, it is also established that the balance between corner-shared and edge-shared GeS4 tetrahedra in the glass backbone of the investigated GeS2-based glasses seems to be responsible for the interconnectivity between two speculative Raman modes at 370 and 430 cm−1. Compositional changes in studied glasses result in the evolution of the observed Raman bands. Such dependences of characteristic constituent Raman bands’ intensities showed that (As2S3)x(GeS2)1−x samples contain different nanophases whose concentration is changing along chosen compositional cross-section.