There is disclosed herein a blood pressure alarm system for use in a dialysis machine whereby alarms may be activated, and a blood pump deactivated if the actual blood pressure increases above or decreases below predetermined levels. The levels are determined by setting a particular blood pressure point and setting the amount by which the pressure can vary above and below the set point; the range of variation is sometimes referred to as the alarm window. A digital memory is provided for storing the set point and preventing variation of the set point with time.