Flow instability conditions, in particular during surge and stall phenomena, have always influenced the operational reliability of turbocompressors and have attracted significant interest resulting in extensive literature. Nowadays, this subject is still one of the most investigated because of its high relevance on centrifugal and axial compressor operating flow range, performance, and efficiency. Many researchers approach this important issue by developing numerical models, whereas others approach it through experimental studies specifically carried out in order to better comprehend this phenomenon. The aim of this paper is to experimentally analyze the stable and unstable operating conditions of an aeronautic turboshaft gas turbine axial–centrifugal compressor installed on a brand new test rig properly designed for this purpose. The test facility is set up in order to obtain (i) the compressor performance maps at rotational speeds up to 25,000 rpm and (ii) the compressor transient behavior during surge. By using two different test rig layouts, instabilities occurring in the compressor, beyond the peak of the characteristic curve, are identified and investigated. These two types of analysis are carried out, thanks to pressure, temperature, and mass flow sensors located in strategic positions along the circuit. These measurement sensors are part of a proper control and acquisition system, characterized by an adjustable sampling frequency. Thus, the desired operating conditions of the compressor in terms of mass flow and rotational speed and transient of these two parameters are regulated by this dedicated control system.