Abstract. The estimation method of the concentration boundary layers thicknesses (δ) in a singlemembrane system containing non-electrolytic binary or ternary solutions was devised using the Kedem-Katchalsky formalism. A square equation used in this method contains membrane transport (L p , σ, ω) and solution (D, C) parameters as well as a volume osmotic flux (J v ). These values can be determined in a series of independent experiments. Calculated values δ are nonlinearly dependent on the concentrations of investigated solutions and the membrane system configuration. These nonlinearities are the effect of a competition between spontaneously occurring diffusion and natural convection. The mathematical model based on Kedem-Katchalsky equations and a concentration Rayleigh number (R C ) was presented. On the basis of this model we introduce the dimensionless parameter, called by us a Katchalsky number (Ka), modifies R C of membrane transport. The critical value of this number well describes a moment of transition from the state of diffusion into convective diffusion membrane transport.