We investigate the hovering dynamics of rigid bodies with up-down asymmetry placed in oscillating background flows. Recent experiments on inanimate pyramid-shaped objects in oscillating flows with zero mean component demonstrate that the resulting aerodynamic forces are sufficient to keep the object aloft. The mechanisms responsible for this lift production are fundamentally unsteady and depend on the shed vorticity. Here, we consider a model system of a two-dimensional flyer and compute the unsteady, two-way coupling between the flyer and the surrounding fluid in the context of the vortex sheet model. We examine in detail the flow properties (frequency and speed) required for hovering and their dependence on the flyer’s characteristics (mass and geometry). We find that, at low oscillation frequencies, a flyer of a fixed mass and shape requires a constant amount of flow acceleration to hover, irrespective of the frequency and speed of the oscillating flow. Meanwhile, at high oscillation frequencies, the flow speed required to hover is constant. In either case, the aerodynamic requirements to hover (flow acceleration or flow speed) are an intrinsic property of the flyer itself. This physical insight could potentially have significant implications on the design of unmanned air vehicles as well as on understanding active hovering of live organisms that can manipulate their flapping motion to favour a larger oscillation amplitude or frequency.