The aim of this study was to evaluate the effect of the addition of hazelnut or walnut flour on the rheological properties of flour and wheat dough (WD). The research material was a system in which wheat flour was replaced with flour based on hazelnuts (HF) or walnuts (WF), i.e., nut flour, in the amounts of 5%, 10% and 15% (WDH, WDW). As a part of the research methodology, we analysed the wet gluten content, and farinographic and extensographic analyses of the dough were performed. Sweep frequency, creep and recovery tests were used to assess the viscoelastic properties of the tested doughs. It was found that the doughs with the addition of walnuts were characterized by different rheological properties compared to the control sample. The systems in which wheat flour was replaced with nuts were characterized by lower water absorption, and this parameter decreased as the share of nuts in the system increased. The mean value of this parameter for WDH was 48.6%, and in the case of WDW it was 47.9%. The development times of WDH and WDW doughs were longer compared to the control, but they decreased as the addition of nut flour was increased. The WDH doughs were characterized by the lowest stability and the highest degree of softening among the examined doughs. It was shown that the addition of nut flour reduced the values of the storage (G′) and loss (G″) modules characterizing the tested doughs, while in each case the G′ value was greater than the G″ value, which proves the advantage of the elastic properties. The creep and recovery tests showed that the nut dough was more susceptible to deformation compared to the control, which indicates that the presence of nut flour weakens the formation of the gluten network forming the dough structure, and makes it more susceptible to stress.