In this paper, we demonstrate a novel self-clocked code-drop unit for incoherent optical code-division multiple-access (CDMA) networks. The unit is based on an all-optical thresholder with internal wavelength conversion that creates a control signal for the drop gate from the incoming data stream. This architecture does not require an external clock signal for drop operation and can be used in asynchronous ring networks. The proposed unit is experimentally demonstrated for two-dimensional time-wavelength optical CDMA codes at a bit rate of 2.5 Gbit/s with two different types of drop gates: terahertz optical asymmetric multiplexer and nonlinear fiber-based loop mirror. Error-free operation is achieved in both configurations. The development of a self-clocked add/drop multiplexer demonstrates a novel concept of asynchronous node operation in multiple access networks.