The features of the process of growth of multilayer heterostructures with InN/InGaN quantum wells (QWs) by the method of molecular-beam epitaxy with nitrogen plasma activation in the mode of modulated metal fluxes are studied. To compensate for elastic stresses in the structure, the active region was formed in the form of an InN/InGaN superlattice matched over the average lattice parameter with the underlying InGaN buffer layer. It has been shown that during the growth of relatively narrow InN QWs up to 3 nm wide, there is no relaxation of elastic stresses in the active region of the structure, and the dislocation density remains at the level N_D~(3-4)·1010 cm-2, which corresponds to the dislocation density in InGaN-buffer. Such structures demonstrate the most intense PL in the wavelength range of 1.3-1.5 μm. With the growth of wider QWs, the imperfection of the structures sharply increases (N_D>1011 cm-2), which is accompanied by a decrease in the emission intensity. The structures grown with InN/InGaN QWs demonstrated an order of magnitude better temperature stability of PL compared to bulk InN layers (PL quenching by ~3 and ~25 times, respectively, in the temperature range of 77-300 K). Nevertheless, at a low temperature (T=77 K), the PL intensity of the studied structures with InN/InGaN QWs is noticeably inferior to that for the bulk InN layer, which apparently indicates a significant role of nonradiative recombination by the Shockley--Reed--Hall mechanism in structures with QWs (as opposed to Auger recombination in bulk InN). Keywords: indium and gallium nitride, molecular beam epitaxy, quantum well, photoluminescence, dislocations.