Sunflower plants (Helianthus annus, var. Russian mammoth) were grown in Hogland nutrient solution. The roots (after being subjected to treatments with either respiratory inhibitors or respiratory stimulators) were used to measure the flux of water Jw, flux of solute Js , and the rate of respiration Jo. The thermodynamic theory of irreversible processes was used to examine the interaction between fluxes, and the changes in conductivity under different treatments. The rate equations for a root membrane of unit thickness were developed as: Jw = LwwVw∆p + LwsRT ln C1s/C2s +LwoRT ln C1o/C2o Js = LswVx∆p + LssRT ln C1s/C2s + LsoRT ln C1o/C2o Jo = LowVw∆p + Los RT ln C1s/C2s + LooRT ln C1o/C2o Where: Lww, Lss, Loo are the direct transfer coefficients for water, solute , and oxygen; and Lws, Lsw, Lwo, Low, Lso, Los are the interaction or linked transfer coefficients; Vw partial molal volume (or specific volume) of water , ∆p the difference in pressure between the external solution and xylem: C1s and C2s , C1o and C2o are the salt and oxygen concentration in external solution and xylem respectively. The results showed that: 1. The nonlinearity of the flux of water through the root system of sunflower is due to causes associated with the membrane (mainly the permeability). 2. The increase in respiration did not increase the permeability of the membrane. 3. The uptake of water due to solute potential under transpiring conditions is small, but important. 4. The uptake of solute in normal root systems is by active process fromsolutions to the zylem and then moves passively to the leaves. 5. An increase in passive water uptake might cause an increase of respiration of the root.