Monitoring system for tubes connecting a patient to a hemodialysis machine incorporates a holder which fixes a section of the tube in the form of a loop (27) which can be tightened by pulling on one end (7) of the tube. Independent claims are included for: (A) a monitoring method for tubes connecting a patient to a hemodialysis machine in which the pressure in the tube is monitored and adjusted within fixed limits by tightening or loosening the loop; and (B) blood treating machines fitted with the system.