The first-principles calculations of the atomic and electronic structure of double-walled nanotubes (DWNTs) of γ-V₂O₅ have been performed and the obtained properties have been compared with those of α-V₂O₅ ones. The DWNT structure relaxation leads to the formation of two types of local regions: (1) adhesion regions and (2) puckering regions. Although the structure of adhesion regions of α-V₂O₅ DWNTs is close to the structure of bulk α-V₂O₅, this is not the case for γ-V₂O₅ DWNTs. The resulting structure of adhesion regions in γ-V₂O₅ SWNTs allows us to assume the existence of hypothetical stable phases, with one of them resembling the experimentally observed R-Nb₂O₅ and (V_0.7Mo_0.3)₂O₅ crystals.