The common assumption when modeling transient liquid flow in an unsaturated porous medium is that the capillary pressure-saturation degree relationship is independent of the macroscopic liquid flux. This assumption is not always applicable, and one reason for this is the dependence of the solid-liquid-gas contact angle at the moving liquid-gaseous interface on the flow velocities, as found in systems such as long cylindrical capillaries. In the present theoretical study, a conjecture is made that at a prescribed capillary pressure the criterion for the liquid phase to invade an empty pore is defined by the Young-Laplace equation, but with the expected dynamic contact angle used instead of the static one. An iterative procedure, based on a simplified description of the pore system, enables a quantitative estimation of the extent of the liquid flux dependence of the capillary pressure-saturation degree relationship. For a given capillary pressure, the degree of liquid saturation decreases with increasing liquid flow velocity, for wetting processes, and vice versa for drainage. This effect of the liquid flux is more pronounced as the width of the pore-size distribution increases.