The invention relates to a device for coning and/or deconing a container unit having corner fittings for the attachment of twist-locks. The device has a support structure for the container unit. The support structure has two parallel long sides and two end sides. According to the invention, the device also includes a storage station that is located adjacent and outside one of the end sides. There is a first conveyor means along a first of the long sides and a second conveyor means along a second of the long sides. Each conveyor means is arranged to transport twist-locks to and from the corner fittings from and to the storage station. The invention also relates to corresponding methods for coning and deconing, respectively.