Membrane distillation carried out in a counter current now module, in which latent heat is recovered by heating the incoming cold seawater with the condensing product water now, is a promising technology for low cost seawater desalination. The membranes used in this module are hydrophobic (polypropylene, polyethylene) and highly permeable fibre membranes. For modelling purposes the Knudsen diffusion and viscous now membrane characteristics (K-0 and B-0 respectively) of five fibre membranes are determined. This paper presents a new, specially developed method for the determination of K-0 and B-0 values of highly permeable fibre membranes with single gas permeation experiments through a short dead end fibre. In order to be able to make use of a reliable method to determine the values of K-0 and B-0, it is essential that the pressure inside the permeable part of the membrane is constant. To determine the conditions at which the pressure drop in the permeable part of the membrane fibre is negligible, this part is reduced in length until the values of K-0 and B-0 become constant. For all membranes the gases He, N-2 and CO2 were used. The gases N-2 and CO2 lead to consistent values of K-0 and B-0. Helium gives less accurate results due to its low molecular weight. The three polypropylene membranes have a similar structure and have therefore about the same values for K-0 and B-0. The same was found for the two polyethylene fibres.