The neoclassical theory of toroidal plasma rotation in the presence of an asymmetric neutral gas source in the edge of tokamak is examined. The poloidal dependence of momentum damping and ion energy loss due to charge-exchange processes are included. It is shown that the toroidal flow velocity increases significantly if the gas is fueled from the inboard side of the tokamak; the radial electric field and its shear are modified accordingly. It is also shown that for a fixed gas-fueling rate, the asymmetric fueling has a smaller role in TEXTOR [G. Mank , Phys. Rev. Lett. 85, 2312 (2000)] than in COMPASS-D [M. Valovi , Plasma Phys. Controlled Fusion 44, A175 (2002)]. The role of asymmetric gas injection is therefore effectively stronger in COMPASS-D. (C) 2004 American Institute of Physics.