Seed storage proteins (gliadins and glutenins) play a key role in the determination of dough and bread-making quality in bread wheat. This is due to the interaction between high and low molecular weight glutenins subunits and gliadins, via complex inter- and intramolecular bondings. In contrast to high molecular weight glutenins, low molecular weight glutenins and gliadins analysis is difficult due to the large number of expressed subunits and coding genes. For these reasons the role of individual proteins/subunits in the determination of wheat quality is less clear. In this work we studied the effect of gene clusters Glu-A3/Gli-A1 and Glu-D3/Gli-D1 in bread-making quality parameters using 20 F4-6 families from the cross Prointa Guazú × Prointa Oasis, both cultivars carrying identical high molecular weight glutenins subunits composition and presence of 1BL/1RS wheat-rye translocation, but differing in Glu-A3/Glu-D3 low molecular weight glutenins subunits and Gli-A1/Gli-D1 gliadins patterns. ANCOVA analysis showed a significant contribution of the Glu-D3/Gli-D1 gene cluster provided by Prointa Guazú to gluten strength explained by mixograph parameters MDS and PW, and Zeleny Test. Markers tagging Prointa Guazú Glu-D3/Gli-D1 alleles are available for strong gluten selection in breeding programs.