The invention concerns a running equation of time mechanism including a hand arrangement whose purpose is to indicate civil time by means of an hour hand and a minute hand, and a true minute hand concentric with the civil minute hand, and which indicates the true solar minute, wherein the running equation of time mechanism also includes an equation of time cam having a profile which is determined by the difference, on each day of the year, between civil time, and true time, wherein this equation of time cam is driven in rotation by a calendar mechanism, wherein the position of the true minute hand is determined by the position of the equation of time cam, wherein the running equation of time mechanism also includes a differential gear device, a first input of which is formed by a civil minute pipe on which a civil minute hand is pressed, and a second input of which is formed by the equation of time cam, wherein the differential gear device includes a planetary reducer wheel set via which the civil minute pipe drives a civil hour pipe on which is pressed the civil hour hand, and a planetary multiplier wheel set via which the civil hour pipe drives a true minute pipe on which is pressed the true minute hand.