Direct interpretation methods for determination of the relative permeability data by linear, non-steady-state, two-phase fluid displacements conducted via constant rate and constant pressure laboratory core tests, are presented. The equations necessary for processing of the displacement test data obtained after the breakthrough of the displacing fluid phase are derived by neglecting the capillary end-effects at sufficiently high flow rates and verified by various experimental data. The total mobility and the mobility ratio of the immiscible fluids are related to the characteristic parameters of the displacement process and the cumulative injected fluid pore volume. The general correlation functions of the characteristic parameters of the immiscible displacement process in porous media are facilitated to conveniently describe the relative permeability functions. These functions allow for accurate determination of the characteristic parameters of immiscible displacement by least-squares linear regression of experimental data. Therefore, the present analytic method determines the relative permeability functions uniquely, rapidly, and more accurately than the previous direct interpretation methods, auxiliary functions, and graphical and analytical methods, and offers a possibility of determining the relative permeability functions from constant pressure and constant rate displacements data.