In this paper, we propose model-based control design strategy for the trajectory tracking of the internet-based bilateral telehaptic systems. The communication time delay between local-master and remote-slave platform is assumed to be symmetrical and unsymmetrical nature. The design comprises delayed position signals with the local velocity signals and the known structure of the master and slave system dynamics. Using Lyapunov-Krasovskii-like functional, asymptotic tracking property of the position and velocity of the master-slave closed-loop systems with symmetric and unsymmetric time varying communication delays are developed. Finally, simulations are conducted to demonstrate the validity of the proposed design for real-time telehaptic operation.