Solute flux in the combined diffusive and convective transport through a homogeneous permselective membrane is a non-linear function of volume flux. A set of linear approximations for this function, which are based on the application of the weighted mean value of boundary solute concentrations for the description of the mean intramembrane concentration, is reviewed. The choice of a particular approximation depends on the range of the Peclet number involved in the investigated problem. Furthermore, it is shown that the original Kedem-Katchalsky formalism, which used a logarithmic mean for the mean intramembrane solute concentration, is a particular case of the general non-linear formalism for zero net solute flux with non-vanishing diffusive and convective fluxes. Thus, the Kedem-Katchalsky logarithmic mean concentration may be used as a linear approximation for the case of diffusive transport in the opposite direction to convective transport. Linear approximations of solute flux equations are also useful for simple phenomenological descriptions of complex membrane systems, which otherwise would need sophisticated mathematical models.