A motor vehicle door lock, such as a motor vehicle bonnet lock includes a locking mechanism which substantially consists of a rotary latch and a pawl. The locking mechanism interacts with a striker element on a bonnet. The lock further has an unlocking/opening mechanism for the bonnet, which mechanism is equipped with a release element provided in the interior of a motor vehicle body. The release element is operated twice to open the bonnet. The locking mechanism is transferred to a pre-latched position after the release element has been operated at least once, with the striker element still being trapped. The bonnet is opened from the pre-latched position by lifting the pawl off the rotary latch with the aid of a power mechanism, said lifting being activated separately.