Mineral-oil based hydraulic fluids are used for power transmission in a number of wide-spread technologies such as hydraulic drives in heavy industrial equipment and construction vehicles as well as automotive systems like power steering and fuel injection. The mathematical modeling of these systems traditionally focuses on the medium to high pressure range where the effects of increased compressiblity due to free air are assumed to be negligible. The goal of the present paper is the precise measurement of the behaviour of a sample of a standard mineral oil based hydraulic fluid under controlled periodic volume change. The fluid is contained in a sealed test chamber equipped with sensors for pressure and temperature as well as a servo-hydraulic actuation system for the controlled volume change. Preliminary results show the expected hysteresis behavior according to the different time scales of the processes of air release and dissolution. Fifty consecutive cycles of compression and decompression are measured in steady state. This collection of measurement data is used for the identification of a dynamic model for the prediction of the amount of free air from the history of pressure change in the system. The fluid used in the tests is an HLP type hydraulic oil with a nominal viscosity of 32 cSt (32*10^-6 m²/s). Absolute pressure values between 0.3 bar and 32 bar (3*10^4 Pa)to 3.2*10^6 Pa) are covered by the published experimental results.