Oil reservoir rocks contain various immiscible fluids (oil, water and gas) and they are submitted to elevated temperatures in the oilfield. Hence, they exhibit a typical coupled behaviour where multiphysics and coupled Thermo-Hydro-Mechanical aspects are predominant. This paper presents some results from researches carried out within the PASACHALK 2 European funded collaborative research. In this research dedicated to subsidence problems in the North sea Ekofisk oilfield, the behaviour of a reservoir chalk containing two immiscible fluids (an organic non polar fluid and water) is considered within the framework of the mechanics of unsaturated soils (no temperature effects considered). In order to account for the mechanical coupled effects related to the two pore fluids, the oil-water suction was considered as an independent stress variable. The paper presents some experimental results describing the combined effect of suction and time on the isotropic compression behaviour of the chalk. A viscoelastoplastic constitutive model based on one hand on the Barcelona BBM elastoplastic model for unsaturated and on the other hand on Perzyna's approach of viscous behaviour of soils is also presented.