In this paper, we present a novel approach for continuous operator authentication in teleoperated robotic processes based on Hidden Markov Models (HMM). While HMMs were originally developed and widely used in speech recognition, they have shown great performance in human motion and activity modeling. We make an analogy between human language and teleoperated robotic processes (i.e. words are analogous to a teleoperator's gestures, sentences are analogous to the entire teleoperated task or process) and implement HMMs to model the teleoperated task. To test the continuous authentication performance of the proposed method, we conducted two sets of analyses. We built a virtual reality (VR) experimental environment using a commodity VR headset (HTC Vive) and haptic feedback enabled controller (Sensable PHANToM Omni) to simulate a real teleoperated task. An experimental study with 10 subjects was then conducted. We also performed simulated continuous operator authentication by using the JHU-ISI Gesture and Skill Assessment Working Set (JIGSAWS). The performance of the model was evaluated based on the continuous (real-time) operator authentication accuracy as well as resistance to a simulated impersonation attack. The results suggest that the proposed method is able to achieve 70% (VR experiment) and 81% (JIGSAW dataset) continuous classification accuracy with as short as a 1-second sample window. It is also capable of detecting the impersonation attack in real-time.