A dialysis machine for treating a body fluid, such as blood or plasma, the dialysis machine comprising: - a dialyzer comprising an enclosure which includes a body fluid passage zone which has a body fluid inlet and a body fluid outlet , and a dialysate passage zone which has a dialysate inlet and a dialysate outlet , and a membrane system between the body fluid passage zone and the dialysate passage zone ; - a dialysate delivery system , - a connection system for connecting a dialysate supply source to the dialysate delivery system , the connection system comprising: - a first section , which comprises a conduit provided at one end with a first connection device which is connectable to a connector of a first dialysate supply source , and which is disconnectable from said connector of the first dialysate supply source , and provided at the other end with a second connection device , said conduit being a flexible conduit of constant cross section in the uncrushed state of said conduit , and - a second section , which comprises a conduit which has one end connected to the dialysate delivery system and which is provided at an opposite end with a connection device which is connected, in a disconnectable manner, to the second connection device of the first section , in order to provide a series connection of the first section and the second section , while allowing said first section to be disconnected from the second section , said conduit of the second section being a flexible conduit of constant cross section in the uncrushed state of said conduit , so that, in the state with the first section disconnected and removed from the second section , said connection device of the second section is connectable to a connector of a second dialysate supply source and disconnectable from said connector of the second dialysate supply source . - a dialyzer comprising an enclosure which includes a body fluid passage zone which has a body fluid inlet and a body fluid outlet , and a dialysate passage zone which has a dialysate inlet and a dialysate outlet , and a membrane system between the body fluid passage zone and the dialysate passage zone ; - a dialysate delivery system , - a connection system for connecting a dialysate supply source to the dialysate delivery system , the connection system comprising: - a first section , which comprises a conduit provided at one end with a first connection device which is connectable to a connector of a first dialysate supply source , and which is disconnectable from said connector of the first dialysate supply source , and provided at the other end with a second connection device , said conduit being a flexible conduit of constant cross section in the uncrushed state of said conduit , and - a second section , which comprises a conduit which has one end connected to the dialysate delivery system and which is provided at an opposite end with a connection device which is connected, in a disconnectable manner, to the second connection device of the first section , in order to provide a series connection of the first section and the second section , while allowing said first section to be disconnected from the second section , said conduit of the second section being a flexible conduit of constant cross section in the uncrushed state of said conduit , <EOS>