Cervical spinal cord injuries (SCIs) often lead to loss of motor function in both hands and legs, limiting autonomy and quality of life. While it was shown that unilateral hand function can be restored after SCI using a hybrid electroencephalography/electrooculography (EEG/EOG) brain/neural hand exoskeleton (B/NHE), it remained unclear whether such hybrid paradigm also could be used for operating two hand exoskeletons, e.g., in the context of bimanual tasks such as eating with fork and knife. To test whether EEG/EOG signals allow for fluent and reliable as well as safe and user-friendly bilateral B/NHE control, eight healthy participants (six females, mean age 24.1 +/- 3.2 years) as well as four chronic tetraplegics (four males, mean age 51.8 +/- 15.2 years) performed a complex sequence of EEG-controlled bilateral grasping and EOG-controlled releasing motions of two exoskeletons visually presented on a screen. A novel EOG command performed by prolonged horizontal eye movements (>1 s) to the left or right was introduced as a reliable switch to activate either the left or right exoskeleton. Fluent EEG control was defined as average "time to initialize" (TTI) grasping motions below 3 s. Reliable EEG control was assumed when classification accuracy exceeded 80%. Safety was defined as "time to stop" (TTS) all unintended grasping motions within 2 s. After the experiment, tetraplegics were asked to rate the user-friendliness of bilateral B/NHE control using Likert scales. Average TTI and accuracy of EEG-controlled operations ranged at 2.14 +/- 0.66 s and 85.89 +/- 15.81% across healthy participants and at 1.90 +/- 0.97 s and 81.25 +/- 16.99% across tetraplegics. Except for one tetraplegic, all participants met the safety requirements. With 88 +/- 11% of the maximum achievable score, tetraplegics rated the control paradigm as user-friendly and reliable. These results suggest that hybrid EEG/EOG B/NHE control of two assistive devices is feasible and safe, paving the way to test this paradigm in larger clinical trials performing bimanual tasks in everyday life environments