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Development of molecular beam epitaxy (MBE) of two-dimensional (2D) layered materials is an inevitable step in realizing novel devices based on 2D materials and heterostructures. However, due to existence of numerous polytypes and occurrence of additional phases, the synthesis of 2D films remains a difficult task. This paper reports on MBE growth of GaSe, InSe, and GaTe layers and related heterostructures on GaAs(001) substrates by using a Se valve cracking cell and group III metal effusion cells. The sophisticated self-consistent analysis of X-ray diffraction, transmission electron microscopy, and Raman spectroscopy data was used to establish the correlation between growth conditions, formed polytypes and additional phases, surface morphology and crystalline structure of the III&ndash, VI 2D layers. The photoluminescence and Raman spectra of the grown films are discussed in detail to confirm or correct the structural findings. The requirement of a high growth temperature for the fabrication of optically active 2D layers was confirmed for all materials. However, this also facilitated the strong diffusion of group III metals in III&ndash, VI and III&ndash, VI/II&ndash, VI heterostructures. In particular, the strong In diffusion into the underlying ZnSe layers was observed in ZnSe/InSe/ZnSe quantum well structures, and the Ga diffusion into the top InSe layer grown at ~450 &deg, C was confirmed by the Raman data in the InSe/GaSe heterostructures. The results on fabrication of the GaSe/GaTe quantum well structures are presented as well, although the choice of optimum growth temperatures to make them optically active is still a challenge.