Abstract: A "dynamically" self-adjusting patient-responsive system for administering liquid medicine such as analgesia to patients as by infusion, with the "demand" of each patient for supplemental doses of drug being taken into account both in providing "on demand" "interval dosing" to supplement a "current rate" of background delivery of the drug to the patient, and in modifying the "current rate" of background delivery of the drug to more correctly correspond to the current needs of a particular patient. While "range" parameters (i.e., "limits" that define acceptable ranges of variance for various characteristics of a program of drug delivery that is intended to meet the very changeable current needs of a particular patient) are preset in accordance with the instructions of a physician, the hour-to-hour manner in which a drug is system-delivered to a particular patient principally is determined on a "dynamic" basis by the extent of the patient's current "demand" for supplemental drug infusion.