In classical fluid lubrication the film thickness is mainly determined by entrainment velocity and oil viscosity. At high pressure, elastic deformation occurs changing the local geometry: this is the elastohydrodynamic lubrication regime (EHL). When a limited amount of lubricant is available to the contact, a component failure due to lubricant starvation can result. A new starvation model is presented, using the amount of oil on the surfaces as the key parameter controlling starvation. It is successfully applied to describe the contacts lubricated with multi-phase fluids such as emulsions and greases, which combine starvation with a very complex rheology