The study was conducted to evaluate the stability of common wheat varieties in four locations with proven different environmental conditions. Three indexes of grain quality were studied: wet gluten content, (WGC); gluten index of grain (GI) and grain sedimentation value (Zeleny). The stability of varieties has been evaluated by many parameters that reflect different aspects of the complete picture for it. The indexes studied are strongly influenced by environmental conditions. The most genetically stable among them is the gluten index (GI), where the genotype has a decisive role of about 70% of the variation, and the most unstable is the wet gluten content (WGC), with only 17% of the effect. As a result of reliable GE, the ranking of the varieties according to the performance of each of the indexes is different in the individual locations. The ranking of varieties in terms of stability according to the ranks of each of the parameters is very different. Even a visual representation of the results, which clears the picture to the maximum extent, shows a different set of stable varieties in each of the quality indexes. Only a few of the varieties (G2, G6, G9, G13, G18, G20, G22) have a good balance between the size and stability of all quality parameters, with a moderate compromise with the grain yield level. The assessment of the stability of the variety in terms of quality can be made according to any of the indexes used. The stability of the variety depends to a large extent on the effect of the environment, which must be considered when selecting a specific index for assessment. The most suitable for this purpose is the gluten index (GI), where the influence of genotype is the strongest, with a significant GE interaction accounting for 25% of all variation. The stability of the variety does not depend on the magnitude of the quality indexes. Stable can be both quality (G2, G6) and varieties with very low grain quality (G18, G20, G22). Stability of quality, at high levels of indexes, is associated with low grain yield and vice versa. From this point of view, combining high yield stability and grain quality at the highest possible levels is a very rare exception (G2, G9).