The local (distributed) behavior of a Kiil dialyser is discussed with the aim of showing the interrelation between the two fluid streams and thus the importance of modeling the system as an interrelated multistream system. A characterization of the dialyser's performance is presented in terms of both an overall log-mean resistance and an effectiveness factor. The effectiveness factor approach gives information on the internal mechanisms and therefore is a better means of both characterizing of Kiil and comparing the performance of different dialysers.