A dialysis machine comprising a haemodialysis filter, an input branch of the dialysing solution into said filter, an output branch of the dialysing solution from the filter, an arterial line which is responsible for conveying the blood from the patient to the filter, a venous line which is responsible for conveying the blood from the filter to the patient, and a plurality of pumps adapted to circulate both the blood and the dialysing solution, an oxygen saturation measuring device applied to the arterial line, and a command/control unit adapted to receive information from the oxygen saturation measuring device and to control other devices of the machine in order to avoid possible cardiovascular failure.