We report on the extensional dynamics of spinning drops in miscible and immiscible background fluids following a rotation speed jump. Two radically different behaviours are observed. Drops in immiscible environments relax exponentially to their equilibrium shape, with a relaxation time that does not depend on the centrifugal forcing.We find an excellent quantitative agreement with the relaxation time predicted for quasi-spherical drops by Stone and Bush (Q. Appl. Math. ,while other models proposed in the literature fail to capture our data. By contrast, drops immersed in a miscible background fluid do not relax to a steady shape: they elongate indefinitely, their length following a power-law l(t) ∼ t 2 5 in very good agreement with the dynamics predicted by Lister and Stone (J. Fluid Mech. , ( )) for inviscid drops. Our results strongly suggest that low compositional gradients in miscible fluids do not give rise to an effective interfacial tension measurable by spinning drop tensiometry. arXiv:1907.02802v1 [cond-mat.soft]