Grain protein fractions have great potential as ingredients that contain high amounts of valuable nutritional components. The aim of this study was to study the rheological behavior of destarched oat and pea proteins and their blends in extrusion-like conditions with a closed cavity rheometer. Additionally, the possibility of producing fibrous structures with high-moisture extrusion from a blend of destarched oat and pea protein was investigated. In the temperature sweep measurement (60–160 °C) of the destarched oat protein concentrate and pea protein isolate blend, three denaturation and polymerization sections were observed. In addition, polymerization as a function of time was recorded in the time sweep measurements. The melting temperature of grain proteins was an important factor when producing texturized structures with a high-moisture extrusion. The formation of fibrillar structures was investigated with high-moisture extrusion from the destarched oat and pea protein blend at temperatures ranging from 140 to 170 °C. The protein–protein interactions were significantly influenced in the extruded samples. This was due to a decrease in the amount of extractable protein in selective buffers. In particular, there was a decrease in non-covalent and covalent bonds due to the formation of insoluble protein complexes.