Two types of supersonic combustion instabilities identified in a M = 2 reacting flow at direct injection of gaseous hydrocarbon fuel and quasi-direct-current (Q-DC) plasma assistance have been considered: a global instability triggered by a mechanism of flow-combustion-plasma coupling and a fast instability of a thermoacoustic nature. The experiments were performed at SBR-50 supersonic combustion facility at variable conditions: pressureP0 = 1-4 bar, temperature T0 = 300-750 K, and fuel mass flow rate m‘ = 1-8.5 g/s. Diagnostics includedpressure measurements, filtered fast camera imaging, schlieren visualization, and spectroscopic observations. The global instability develops with a characteristic time of about 10 ms and is related to the interaction of the combustion-based separation zone with the reflected shock wave (SW) and electric discharge. It is shown that this instability could be effectively controlled by electrical discharge power. The thermoacoustic instability is developed with a characteristic time less than 1 ms. The analysis of pressure data reveals a resonant acoustic wave presence in the combustion zone between the fuel injection ports and the test section diffuser.