Continuous mathematical expressions of the soil hydraulic functions, namely, the water retention curve (WRC) and the relative hydraulic conductivity function (RHC), are indispensable for the solution of the equations describing flow processes in soils. The WRC model of Brooks and Corey is a widely used empirical, easy to derive but discontinuous expression that introduces the pore size distribution index, λ, and Mualem's approach is widely used to predict the RHC in terms of the WRC. When this approach is applied to the Brooks and Corey expression, the prediction of the RHC depends solely on λ. The present study used measured hydraulic functions of a wide range of soil types to derive parameter equivalence between the parameters ψc and λ of the Brooks and Corey expression and the parameters ξ and ¿ of the continuous expression that results from the WRC model of Assouline et al. Strong relationships were found between ¿ and λ and between ξ and (ψc-λ). Also, it was found that λ is inversely proportional to the coefficient of variation, $varepsilon$, of the WRC. On the basis of a previous relationship between the parameter η in the RHC model of Assouline and $varepsilon$ a relationship between λ and η is derived. This leads to a new simple expression for the prediction of the RHC.