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Hinged constructions in Rd having pinned joints and admitting internal stresses are studied. A conjecture about the existence of a restoring stress for a linear framework restorable by its internal stress space is proved. In the case of arbitrary dimension, a sufficient condition for the existence of a restoring stress is given. A number of properties of the set of frameworks restorable by an internal stress are established. New problems are formulated. Bibliography: 7 titles.