Recently we have shown that the unshocked winds of pulsars could be directly observed through its inverse Compton (IC) &ggr;-ray emission caused by illumination of the wind by low-frequency photons emitted by the surface of the neutron star or by the pulsar’s magnetosphere [1]. Limitations imposed by present &ggr;-ray observations of the Crab Nebula on the wind acceleration mechanisms are discussed. In particular, the comparison of the upper limits on pulsed TeV &ggr;-ray emission from the Crab with the calculated IC &ggr;-ray fluxes excludes the possibility of formation of the kinetic-energy-dominated wind with Lorentz factor&ggr;W⩾106within 30 light-cylinder radii of the pulsar, provided that the soft nonthermal emission is produced inside the light cylinder. At the same time, the acceleration of the wind on the light cylinder is allowed under a radical assumption that the production of the soft nonthermal emission and the acceleration of the wind occur in the same place. If so, the remarkable IC signatures of the pulsar winds could be revealed, under certain conditions, by current and planned space- and satellite-based high energy &ggr;-ray detectors. ©2001 American Institute of Physics.