The output-feedback design problem for a bilateral teleoperator scheme is considered. The recently proposed Immersion and Invariance (I&I) observer is used to obtain an exponentially convergent estimate of the unmeasured velocities. Moreover, it is proven that when this observer is interconnected to the nonlinear teleoperator together with a Proportional plus damping (P+d) controller, the overall system is globally stable. Finally, in the case when the human operator and the environment do not exert forces on the local and remote manipulator, respectively, global asymptotic convergence to zero of the velocities and of the position tracking error is achieved. These results are obtained by introducing two important design modifications ensuring the explicit derivation of the observer dynamics and that the interconnected system inherits the same stability properties as in the full-measurement case. The theoretical results are illustrated with simulations using local and remote two degree-of-freedom nonlinear manipulators.