A display device, comprising: - a first rotary display organ displaying the hour associated with an hours wheel that is kinematically connected to a cannon-pinion, - a second rotary display organ displaying the minute, secured to a minutes wheel kinematically connected to the cannon-pinion, - a dial on which hours appear, - mechanical means (70, 71, 80, 81) for modifying the position of said first display organ, arranged to drive a movement of said first display organ from a position according to a standard display to a phase-shifted position displaying a non-real time, and vice versa, when said modification means are actuated; - mechanical phase-shift means (56, 56') of said first display organ arranged to transmit, to said first display organ, the movement of the cannon-pinion when said mechanical modification means are not actuated and to transmit, to said first display organ, a rotation movement different from that imposed by the cannon-pinion, when said mechanical modification means are actuated and cooperate with said phase-shift means to move said first display organ from its standard position to its phase-shifted position, and vice versa; - actuating means (74, 84) of said mechanical modification means (70, 71, 80, 81); and - control means (76, 86) of said actuating means (74, 84) arranged to allow a user to activate said actuating means and to take the first display organ from its position according to the standard display to its phase-shifted position, and vice versa, characterized in that the phase-shift means of the first display organ comprise a first differential gear kinematically connected by a first input to the cannon-pinion, by a second input to the mechanical modification means (70, 71; 80, 81) of the position of the first display organ, and by an output to said hours wheel supporting said first display organ. - a first rotary display organ displaying the hour associated with an hours wheel that is kinematically connected to a cannon-pinion, - a second rotary display organ displaying the minute, secured to a minutes wheel kinematically connected to the cannon-pinion, - a dial on which hours appear, - mechanical means (70, 71, 80, 81) for modifying the position of said first display organ, arranged to drive a movement of said first display organ from a position according to a standard display to a phase-shifted position displaying a non-real time, and vice versa, when said modification means are actuated; - mechanical phase-shift means (56, 56') of said first display organ arranged to transmit, to said first display organ, the movement of the cannon-pinion when said mechanical modification means are not actuated and to transmit, to said first display organ, a rotation movement different from that imposed by the cannon-pinion, when said mechanical modification means are actuated and cooperate with said phase-shift means to move said first display organ from its standard position to its phase-shifted position, and vice versa; - actuating means (74, 84) of said mechanical modification means (70, 71, 80, 81); and - control means (76, 86) of said actuating means (74, 84) arranged to allow a user to activate said actuating means and to take the first display organ from its position according to the standard display to its phase-shifted position, and vice versa,