The instantaneous tangential rigidity (corresponding to the applied horizontal load) of a triguy support with unequal ropes is determined. The differences between the ropes can be due to the different location, both horizontal and vertical, of their anchoring foundations and to the different types of ropes used. The horizontal rigidity of such a support has no general axis of symmetry. Therefore a formula for this rigidity in any direction and a formula for extreme rigidity angles are given in this paper. A notion of the guy’s eigenvalue, standing for the initial tension force above which the guy participates effectively in the support’s rigidity, is introduced. A numerical example is provided.