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Abstract. Let G be a compact connected Lie group G and T its maximal torus. The coadjoint orbit Oλ through λ ∈ t ∗ is canonically a symplectic manifold. There-fore we can ask the question of its Gromov width. In many known cases the width is exactly the minimum over the set {〈α∨j, λ〉;α∨j a coroot, 〈α∨j, λ 〉> 0}. We will show that the Gromov width for regular coadjoint orbits of the special orthogonal group is at least this minimum. The proof uses the torus action coming from the Gelfand-Tsetlin system