The analysis of signals of surges and rotating stalls occurring and processing is essential to reveal the characteristics of instability phenomena, to develop detecting methodology and active control technique, to assure the rig and compressor safety. A highspeed 7-stage compressor was tested on a rig, with 10 channels of casing static pressures and a channel of outlet total pressure. It illustrates by the case with the rotating speed 16,400RPM. Firstly, to detect the stall precursors, the spectrum analysis and the short-time-Fourier-transform (STFT) are employed. It shows the precursors are formed about 3.5s before the surge point in each stage individually. Then, the correlation functions are calculated to analysis the relationship between casing static pressures. Results show that the rotating stalls of the 1-3stages have phase differences, while the 4-7stages do not. Finally, the time-domain waveforms analysis instruct that the stagnation cell of surge is firstly formed between the 3 rd and the 4 th stator rows, and then moves downwards. The surge is companied with the rotating stalls. The front 3 stages are in the cycles of the stall-surge-recoverstall in the whole surge process.