In this paper, we discuss the problem of instability in the dimension of a spline space over a T-mesh. For bivariate spline spaces S (5, 5, 3, 3) and S (4, 4, 2, 2), the instability in the dimension is shown over certain types of T-meshes. This result could be considered as an attempt to answer the question of how large the polynomial degree (m,m′) should be relative to the smoothness (r, r′ ) to make the dimension of a spline space stable. We show in particular that the bound m≥2r+1and m′ ≥2r′ +1are optimal.