This paper deals with nonconservative mechanical systems subjected to nonconservative positional forces leading to nonsymmetric tangential stiffness matrices. The geometric degree of nonconservativity of such systems is then defined as the minimal number ℓℓ of kinematic constraints necessary to convert the initial system into a conservative one. Finding this number and describing the set of corresponding kinematic constraints is reduced to a linear algebra problem. This index ℓℓ of nonconservativity is the half of the rank of the skew-symmetric part KaKa of the stiffness matrix KK that is always an even number. The set of constraints is extracted from the eigenspaces of the symmetric matrix K2aKa2. Several examples including the well-known Ziegler column illustrate the results.