In order to effectively monitor the operational status and detect faults within a hybrid electric vehicle during mode transitions, this study focuses on a specific power-split hybrid electric vehicle model known as the multimode electromechanical composite transmission system (MM-EMCTS HEV). Taking into account the actual occurrence frequency and simulatability of faults in MM-EMCTS HEV, key faults are extracted. Based on the distinctive characteristics and properties of critical system faults, a fault diagnosis framework is constructed by leveraging global analytical redundancy relations (GARRs). This framework encompasses strategies for residual generation across sensors, actuators, and controlled components, alongside residual evaluation techniques employing mode-dependent adaptive thresholds. The detectability and isolatability of the MM-EMCTS are thoroughly analyzed. Subsequently, simulation and verification of the residual responses under typical faults in the MM-EMCTS are implemented in Matlab/Simulink and Simscape. The results demonstrate the efficacy of the fault diagnosis method, rooted in global analytical redundancy relations and mode-dependent adaptive thresholds, in successfully detecting and isolating faults within multimode electromechanical composite transmission systems. Furthermore, compared to conventional fixed threshold residual evaluation approaches, this method significantly mitigates the occurrence of missed detections, thus verifying the effectiveness and superiority of the proposed method.