An electromagnetic clutch comprising: a driving rotary element and a driven rotary element mounted coaxially with a rotational axis; a coiled wrap spring centering about the rotational axis; and a control mechanism for switching the electromagnetic clutch between a transmission state for bring the wrap spring into pressure contact with the driving rotary element by changing a winding diameter of the wrap spring to transmit a rotational force of the driving rotary element to the driven rotary element, and a cutoff state for decreasing the pressure contact force of the wrap spring against the driving rotary element thereby to cut off the rotational force transmitted to the driven rotary element; wherein the control mechanism includes a driving element connected to one end of the wrap spring to be rotatable in unison with the driven rotary element, an operating element made of magnetic material and connected to the other end of the wrap spring to be rotatable about the rotational axis, and an electromagnetic solenoid supported to a stationary element for attracting the operating element to restrain the operating element, the control mechanism further includes restraint means for allowing rotation of the driving element caused by dynamic inertia after the operating element is restrained by the attraction of the electromagnetic solenoid in the transmission state to achieve a rotational phase in which the driving rotary element is brought to the cutoff state and then restraining the driving element, the driven rotary element is formed as a shaft, the operating element is mounted on the shaft to be relatively rotatable and displaceable along the rotational axis, an armature made of magnetic material is provided to face the electromagnetic solenoid across the operating element to be rotatable in unison with the shaft and displaceable along the rotational axis, characterized in that the restraint means includes the operating element and the armature, in which a main aperture is formed in a surface of the operating element for attracting the electromagnetic solenoid and an auxiliary aperture is formed in a surface of the armature on which magnetic flux from the operating element is exerted, the main aperture and the auxiliary aperture achieving a positional relationship to allow a drawing force exerted on the armature to increase when the rotational phase in which the driving rotary element is brought to the cutoff state is achieved, after the operating element is attracted to the electromagnetic solenoid, and then attract and restrain the armature to the operating element by the increased drawing force. a driving rotary element and a driven rotary element mounted coaxially with a rotational axis; a coiled wrap spring centering about the rotational axis; and a control mechanism for switching the electromagnetic clutch between a transmission state for bring the wrap spring into pressure contact with the driving rotary element by changing a winding diameter of the wrap spring to transmit a rotational force of the driving rotary element to the driven rotary element, and a cutoff state for decreasing the pressure contact force of the wrap spring against the driving rotary element thereby to cut off the rotational force transmitted to the driven rotary element; wherein the control mechanism includes a driving element connected to one end of the wrap spring to be rotatable in unison with the driven rotary element, an operating element made of magnetic material and connected to the other end of the wrap spring to be rotatable about the rotational axis, and an electromagnetic solenoid supported to a stationary element for attracting the operating element to restrain the operating element, the control mechanism further includes restraint means for allowing rotation of the driving element caused by dynamic inertia after the operating element is restrained by the attraction of the electromagnetic solenoid in the transmission state to achieve a rotational phase in which the driving rotary element is brought to the cutoff state and then restraining the driving element, the driven rotary element is formed as a shaft, the operating element is mounted on the shaft to be relatively rotatable and displaceable along the rotational axis, an armature made of magnetic material is provided to face the electromagnetic solenoid across the operating element to be rotatable in unison with the shaft and displaceable along the rotational axis, characterized in that the restraint means includes the operating element and the armature, in which a main aperture is formed in a surface of the operating element for attracting the electromagnetic solenoid and an auxiliary aperture is formed in a surface of the armature on which magnetic flux from the operating element is exerted, the main aperture and the auxiliary aperture achieving a positional relationship to allow a drawing force exerted on the armature to increase when the rotational phase in which the driving rotary element is brought to the cutoff state is achieved, after the operating element is attracted to the electromagnetic solenoid, and then attract and restrain the armature to the operating element by the increased drawing force.