Boolean logic circuits comprising nanotube-based switching elements with multiple controls. The Boolean logic circuits include input and output terminals and a network of nanotube switching elements electrically disposed between said at least one input terminal and said output terminal. Each 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 along the nanotube channel element. At least one nanotube switching element non-volatilely retains an informational state and at least one nanotube switching elements volatilely retains an informational state. The network of nanotube switching elements effectuates a Boolean function transformation of Boolean signals on said at least one input terminal. Dual rail cascode logic circuits may also be constructed from the nanotube switching elements.