A running equation of time mechanism includes civil hour and minute hands to indicate civil time and a concentric true minute hand to indicate true time. The running equation of time mechanism includes an equation of time cam and 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. 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.