Nonstoichiometric GeSixOy glass films and many-layer structures based on them were obtained by high-vacuum electron beam vapor deposition (EBVD). Using EBVD, the GeO2, SiO, SiO2, or Ge powders were co-evaporated and deposited onto a cold (100 °C) p+-Si(001) substrate with resistivity ρ = 0.0016 ± 0.0001 Ohm·cm. The as-deposited samples were studied by Fourier-transformed infrared spectroscopy, atomic force microscopy, X-ray photoelectron spectroscopy, and Raman spectroscopy. A transparent indium–tin–oxide (ITO) contact was deposited as the top electrode, and memristor metal–insulator–semiconductor (MIS) structures were fabricated. The current–voltage characteristics (I–V), as well as the resistive switching cycles of the MIS, have been studied. Reversible resistive switching (memristor effect) was observed for one-layer GeSi0.9O2.8, two-layer GeSi0.9O1.8/GeSi0.9O2.8 and GeSi0.9O1.8/SiO, and three-layer SiO2/a–Ge/GeSi0.9O2.8 MIS structures. For a one-layer MIS structure, the number of rewriting cycles reached several thousand, while the memory window (the ratio of currents in the ON and OFF states) remained at 1–2 orders of magnitude. Intermediate resistance states were observed in many-layer structures. These states may be promising for use in multi-bit memristors and for simulating neural networks. In the three-layer MIS structure, resistive switching took place quite smoothly, and hysteresis was observed in the I–V characteristics; such a structure can be used as an “analog” memristor.