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As life expectancy is mostly increasing, the incidence of many neurological disorders is also constantly growing. For improving the physical functions affected by a neurological disorder, rehabilitation procedures are mandatory, and they must be performed regularly. Unfortunately, neurorehabilitation procedures have disadvantages in terms of costs, accessibility and a lack of therapists. This paper presents Immersive Neurorehabilitation Exercises Using Virtual Reality (INREX-VR), our innovative immersive neurorehabilitation system using virtual reality. The system is based on a thorough research methodology and is able to capture real-time user movements and evaluate joint mobility for both upper and lower limbs, record training sessions and save electromyography data. The use of the first-person perspective increases immersion, and the joint range of motion is calculated with the help of both the HTC Vive system and inverse kinematics principles applied on skeleton rigs. Tutorial exercises are demonstrated by a virtual therapist, as they were recorded with real-life physicians, and sessions can be monitored and configured through tele-medicine. Complex movements are practiced in gamified settings, encouraging self-improvement and competition. Finally, we proposed a training plan and preliminary tests which show promising results in terms of accuracy and user feedback. As future developments, we plan to improve the system's accuracy and investigate a wireless alternative based on neural networks.