This paper addresses problems to achieve transparency and contact stability for teleoperation that consists of unconstrained and constrained motions. The adaptive bilateral control with a local force compensator is developed, based on adaptive impedance control and contact force driven compensation with auto-switching functions. Without any knowledge about robotic and environment dynamics and with a communication delay, the developed method guarantees good adaptive tracking performance in unconstrained motion and reduction of oscillating contacts in constrained motion. Based on an actual haptic device and a virtual manipulator, haptic simulations are presented to demonstrate adaptive transparency and contact stability in the presence of communication delay.