In this paper we study growth of quasi-one-dimensional GaN nanowires (NWs) and nanotube (NT)-like nanostructures on Si(111) substrates covered with a thin AlN layer grown by means of plasma-assisted molecular beam epitaxy. In the first part of our study we investigate the influence of the growth parameters on the geometrical properties of the GaN NW arrays. First, we find that the annealing procedure carried out prior to deposition of the AlN buffer affects the elongation rate and the surface density of the wires. It has been experimentally demonstrated that the NW elongation rate and the surface density drastically depend on the substrate growth temperature, where 800 °C corresponds to the maximum elongation rate of the NWs. In the second part of the study, we introduce a new dopant-stimulated method for GaN nanotube-like nanostructure synthesis using a high-intensity Si flux. Transmission electron microscopy was used to investigate the morphological features of the GaN nanostructures. The synthesized structures have a hexagonal cross-section and possess high crystal quality. We propose a theoretical model of the novel nanostructure formation which includes the role of the dopant Si. Some of the Si-doped samples were studied with the photoluminescence (PL) technique. The analysis of the PL spectra shows that the highest value of donor concentration in the nanostructures exceeds 5·10 ¹⁹ cm ^-3.