We investigate the electrohydrodynamics of an initially spherical droplet under the influence of an external alternating electric field by conducting axisymmetric numerical simulations using a charge-conservative volume-of-fluid based finite volume flow solver. The mean amplitude of shape oscillations of a droplet subjected to an alternating electric field for leaky dielectric fluids is similar to the steady-state deformation under an equivalent root mean squared direct electric field for all possible electrical conductivity ratio (Formula presented.) and permittivity ratio (Formula presented.) of the droplet to the surrounding fluid. In contrast, our simulations for weakly conducting media show that this equivalence between alternating and direct electric fields does not hold for (Formula presented.). Moreover, for a range of parameters, the deformation obtained using the alternating and direct electric fields is qualitatively different, that is, for low (Formula presented.) and high (Formula presented.), the droplet becomes prolate under alternating electric field but deforms to an oblate shape in the case of the equivalent direct electric field. A parametric study is conducted by varying the time period of the applied alternating electric field, the permittivity and the electrical conductivity ratios. It is observed that while increasing (Formula presented.) has a negligible effect on the deformation dynamics of the droplet for (Formula presented.), it enhances the deformation of the droplet when (Formula presented.) for both alternating and direct electric fields. We believe that our results may be of immense consequence in explaining the morphological evolution of droplets in a plethora of scenarios ranging from nature to biology. © 2020 Wiley-VCH GmbH