A floating system for very deep water includes a floating structure (1) subject to the external loadings (7, 8, 9) inducing stresses, the floating structure (1) being held in position on the sea bed by one or several tensioned lines (2) made of a material having given mechanical properties. The tensioned line or lines (2) are made of a material that is not very sensitive to fatigue stresses and the tensioned line or lines are sized in a manner independent of the fatigue phenomena associated with the dynamic behavior of the floating system under the effect of external loadings.