Abstract: Data on the synthesis of structures for a quantum cascade terahertz laser in the AlGaAs/GaAs material system on GaAs substrates using the molecular-beam-epitaxy method and their characterization are presented. The specific features necessary for the implementation of such structures are considered. It is shown that, for this configuration, almost single-mode lasing is observed at a frequency of ~3 THz up to a temperature of ~60 K.