In automatic guidance of agriculture vehicles, lateral control is not the only requirement. Much research work has been focused on trajectory tracking control which can provide high longitudinal-lateral control accuracy. Satisfactory results have been reported as soon as vehicles move without sliding. But unfortunately pure rolling constraints are not always satisfied especially in agriculture applications where working conditions are rough and not predictable. In this paper the problem of trajectory tracking control of autonomous farm vehicles in the presence of sliding is addressed. To take sliding effects into account, three variables which characterize sliding effects are introduced into the kinematic model based on geometric and velocity constraints. With a linearized approximation, a refined kinematic model is obtained in which sliding effects appear as additive unknown parameters to the ideal kinematic model. By an integrating parameter adaptation technique with a backstepping method, a stepwise procedure is proposed to design a robust adaptive controller in which time-invariant sliding is compensated for by parameter adaptation and time-varying sliding is corrected by a Variable Structure Controller (VSC). It is theoretically proven that for farm vehicles subjected to sliding, the longitudinal-lateral deviations can be stabilized near zero and the orientation errors converge into a neighborhood near the origin. To be more realistic for agriculture applications, an adaptive controller with projection mapping is also proposed. Both simulation and experimental results show that the proposed (robust) adaptive controllers can guarantee high trajectory tracking accuracy regardless of sliding.