Hybrid switching devices integrate nanotube switching elements with field effect devices, such as NFETs and PFETs. A switching device forms and unforms a conductive channel from the signal input to the output subject to the relative state of the control input. In embodiments of the invention, the conductive channel includes a nanotube channel element and a field modulatable semiconductor channel element. The switching device may include a nanotube switching element and a field effect device electrically disposed in series. According to one aspect of the invention, an integrated switching device is a four-terminal device with a signal input terminal, a control input terminal, a second input terminal, and an output terminal. The devices may be non-volatile. The devices can form the basis for a hybrid NT-FET logic family and can be used to implement any Boolean logic circuit.