Plant breeders have long sought to develop lines that combine outstanding performance with high and stable quality in different environments. The high-arabinoxylan (AX) Chinese variety Yumai-34 was crossed with three Central European wheat varieties (Lupus, Mv-Mambo, Ukrainka) and 31 selected high-AX lines were compared for physical (hectolitre weight, thousand grain weight, flour yield), compositional (protein content, gluten content, pentosan) and processing quality traits (gluten index, Zeleny sedimentation, Farinograph parameters) in a three-year experiment (2013-2015) in the F7-F9 generations. The stability and heritability of different traits, including the relative effects of the genotype (G) and environment (E), were determined focusing on grain composition. The contents of total and water-soluble pentosans were significantly affected by G, E and G × E interactions, but the heritability of total (TOT)-pentosan was significantly lower (0.341) than that of water-extractable (WE)-pentosan (0.825). The main component of the pentosans, the amount and composition (arabinose:xylose ratio) of the arabinoxylan (AX), was primarily determined by the environment and, accordingly, the broader heritability of these parameters were 0.516 and 0.772. However, genotype significantly affected the amount of water-soluble arabinoxylan and its composition and thus the heritability of these traits was also significant (0.840 and 0.721). The genotypes exhibiting higher stability of content of TOT-pentosan also showed more stable contents of WE-pentosan. There was a positive correlation between the stability of contents of WE-pentosan and WE-AX, while the stability of the WE-AX content and AX composition were also strongly correlated. Water absorption was strongly genetically determined with a heritability of 0.829 with the genotype determining 38.67% of the total variance. Many lines were grouped in the GGE biplot, indicating that they did not significantly differ stability.