Access security system with the following elements: - Multiple stationary containers, each of which comprises a locking device, which is unlockable to selectively enable access to an interior space of said container, and wherein each of the stationary containers has been assigned a container identification feature; - a stationary security module inside each container, which comprises a security key generator and an authorisation module; - a mobile authorisation key supply unit with a storage device and a communication module to supply an authorisation key to the authorisation module; - wherein each authorisation module is arranged to compare the security key produced by the security key generator with the supplied authorisation key from the authorisation key supply unit and in the case of matching each other, to produce a signal to unlock the locking device, - furthermore, with a remote computing system, which is equipped with an authorisation key generator and is capable of communicating with the authorisation key supply unit at least for the transfer of authorisation keys to the authorisation key supply unit, - wherein the authorisation key supply unit is selectively operable in an online mode, in which the communication between the authorisation key supply unit and the remote computing system is presumed to be secured, and in an offline mode, in which the communication between the authorisation key supply unit and the remote computing system is not secured, wherein each container identification feature is linked to a communication feature that indicates either the online or offline mode for the container identification feature corresponding to the stationary container, and wherein the access security system is arranged so that the offline or online mode is indicated in advance through determining the quality of the communication between the authorisation key supply unit and the remote computing system, wherein those authorisation keys that are linked to a container identification feature indicating the offline mode as a communication feature will be filed in advance to the storage device of the authorisation key supply unit and upon entering the container identification feature are retrievable from the storage device of the authorisation key supply unit. - Multiple stationary containers, each of which comprises a locking device, which is unlockable to selectively enable access to an interior space of said container, and wherein each of the stationary containers has been assigned a container identification feature; - a stationary security module inside each container, which comprises a security key generator and an authorisation module; - a mobile authorisation key supply unit with a storage device and a communication module to supply an authorisation key to the authorisation module; - wherein each authorisation module is arranged to compare the security key produced by the security key generator with the supplied authorisation key from the authorisation key supply unit and in the case of matching each other, to produce a signal to unlock the locking device, - furthermore, with a remote computing system, which is equipped with an authorisation key generator and is capable of communicating with the authorisation key supply unit at least for the transfer of authorisation keys to the authorisation key supply unit, - wherein the authorisation key supply unit is selectively operable in an online mode, in which the communication between the authorisation key supply unit and the remote computing system is presumed to be secured, and in an offline mode, in which the communication between the authorisation key supply unit and the remote computing system is not secured, wherein each container identification feature is linked to a communication feature that indicates either the online or offline mode for the container identification feature corresponding to the stationary container, and wherein the access security system is arranged so that the offline or online mode is indicated in advance through determining the quality of the communication between the authorisation key supply unit and the remote computing system, wherein those authorisation keys that are linked to a container identification feature indicating the offline mode as a communication feature will be filed in advance to the storage device of the authorisation key supply unit and upon entering the container identification feature are retrievable from the storage device of the authorisation key supply unit.