Nanotube-based switching elements with multiple controls and circuits made from such. A switching element includes an input node, an output node, and a nanotube channel element having at least one electrically conductive nanotube. A control structure is disposed in relation to the nanotube channel element to controllably form and unform an electrically conductive channel between said input node and said output node. The output node is constructed and arranged so that channel formation is substantially unaffected by the electrical state of the output node. The control structure includes a control electrode and a release electrode, disposed on opposite sides of the nanotube channel element. The control and release may be used to form a differential input, or if the device is constructed appropriately to operate the circuit in a non-volatile manner. The switching elements may be arranged into logic circuits and latches having differential inputs and/or non-volatile behavior depending on the construction.