The use of the oscillating drop method for measuring the deformation retardation time lambda(2) of viscoelastic liquids is proposed. For small oscillation amplitudes, lambda(2) may be determined from the characteristic equation of the drop derived from linear theory. In the experiment an acoustically levitated individual drop is excited to shape oscillations of the fundamental mode m = 2 by ultrasound modulation. Once the excitation is terminated, the drop performs damped oscillations, and the angular frequency and damping rate are measured from drop shapes recorded by a high-speed camera. A numerical method is used for determining a pair of liquid properties from the characteristic equation - the liquid zero-shear dynamic viscosity eta(0) and the deformation retardation time lambda(2). The spherical Bessel functions involved in the equation produce a manifold of solutions, from which the correct one must be identified. Comparison of the computed value of eta(0), with the result from a rheometric liquid characterisation is found to be the right criterion for the identification. The values of lambda(2) obtained by this measurement are found to depend weakly on uncertainties of the experiment. They deviate strongly from the values typically used in simulations of viscoelastic liquid flow. (C) 2015 Elsevier B.V. All rights reserved.