This work considers the control of nonlinear bilateral teleoperators with variable time delays without the need of velocity measurements. The recently proposed Immersion and Invariance observer is used to obtain an exponentially convergent estimate of the unmeasured velocities. Under the classical assumption that the human operator and the environment define passive, velocity to force, maps, it is proved that with this observer and a Proportional plus damping controller, velocities and position error are globally bounded. Finally, in the case that the human operator and the environment do not exert forces on the local and remote manipulators, respectively, global asymptotic convergence of velocities and of position error to zero is achieved. The theoretical results are sustained with simulations using a couple of two degrees-of-freedom nonlinear manipulators.