The objective of this research was to evaluate the rheological and textural properties of gluten-free doughs based on potato starch, which was partially substituted by different proportions of quinoa (10%, 30% and 50%), kiwicha (10%, 30% and 50%) or tarwi flour (10%, 20% and 30%). The influence of the substitution on the kinetics of the leavening process was studied as well. The back-extrusion technique was used to determine rheological and textural properties of the dough, and the leavening kinetics were modelled using the Gompertz equation. The results showed that textural properties such as firmness, consistency, cohesiveness and viscosity index, as well as the consistency index of the doughs increased as the level of substitution of the Andean grain flour in the formulation increased. It was determined that the formulations with an addition of 10% and 20% for quinoa or kiwicha flour, and 10% for tarwi flour would be most suitable for developing gluten-free breads.