The problem of controlling a rigid bilateral teleoperator has been the subject of study since the late 1980s and several control approaches have been reported to deal with time-delays, position tracking and transparency. However, the general flexible case is still an open problem. The present paper reports an adaptive and damping injection controller and a proportional plus damping injection (P +d) controller which are capable of globally stabilizing a nonlinear bilateral teleoperator with joint flexibility and time-delays. More precisely, the adaptive scheme is able to cope with uncertainty in the parameters and constant timedelays, while the P + d scheme is shown to treat variable time-delays. In both cases, the teleoperator is composed of a rigid local manipulator and a flexible joint remote manipulator. The extension to the case where the local and remote manipulators exhibit joint flexibility is also reported using the P +d scheme. Under the common assumption that the human operator and the environment are passive it is proven, for the P +d schemes, that the joint and actuator velocities as well as the local and remote position errors are bounded. Moreover, if the human operator and remote environment forces are zero then, for both controllers, position tracking is established and local and remote velocities asymptotically converge to zero. Simulations and experiments are presented to depict the performance of the proposed schemes.