Selective laser melting technology has the ability to directly produce finished parts, and is economically efficient for single or small batch production. Copper and its alloys are of great interest due to their high thermal and electrical conductivity. The influence of build process parameters, such as scanning speed and layer thickness on the stability of single track formation using a heat-resistant copper alloy PR-BrKh was investigated in this paper. The mechanism of single track formation was studied. As a result, patterns of formation of a stable single track were established, the upper and lower limits of the build parameters were determined. The results of the study provide a deeper understanding of the copper alloys selective laser melting process and may serve as a basis for determining the optimal parameters’ range for ‘growing’ solid structures.