A time-dependent resistance model is used to study haemodynamic aspects of haemodialysis treatment. In the first part of the paper one model circuit, consisting of a pressure source, upstream and downstream resistances and a branching resistance, is shown to represent the haemodynamics of any type of arteriovenous fistula (AVF). Simple algebraic relations are derived for the haemodynamic determinants of AVFS, including finger ischaemia and AVF-maturation. The second part of the paper analyses the influences of a two-needle extracorporeal dialysis (ECD) circuit on the systemic vascular haemodynamics. The main result of the analysis is that the ECD-circuit can be considered as virtually independent of the systemic circulation. Consequently the dialysis flow does not depend on systemic vascular determinants and there are no instantaneous changes in the systemic circulation after switching on the ECD circuit. The ECD flow at onset of AVF collapse is shown to be (slightly) larger than the undisturbed AVF flow. Hence, onset of collapse strongly depends on the systemic blood pressure and vascular resistances. It can be used diagnostically to assess AVF capacities. Optimisation of haemodialysis through the ECD circuit is predicted to be inefficient.