Relative perturbation bounds for stable linear gyroscopic systems Mẍ(t)+Gẋ(t)+Kx(t)=0 are considered, where M,K∈Rn×n are symmetric, M is positive definite, K negative definite and G∈Rn×n is skew-symmetric such that |G|>kM−k−1K for some k>0. This means that all of the eigenvalues of the system are purely imaginary and semi-simple. For this kind of systems, we present an upper bound for the relative change in eigenvalues as well as the sinΘ type bound for the corresponding eigenvectors under the perturbation of the system matrices. The performance of obtained bounds is illustrated in numerical experiments.