Current-voltage equations have been derived for metal-insulator-semiconductor-insulator-metal inversion-type field-effect transistors (MISIM-FET's) in thin layers of single-crystal silicon. These dc equations, based on the depletion approximation and the gradual channel approximation, describe the effects of the "back" MIS gate on the "front" MIS channel in the triode region of strong-inversion operation. When the thickness of the silicon is less than twice the depletion depth, the front and back channels can interact. The de effects are a variation in the channel current and drain saturation voltage of one channel with voltage applied to the opposite gate. These models account for front-back channel interactions apparent in the MISIM-FET tetrode structure which cannot be modeled by one-sided MOS theory. In addition, they offer speed and simplicity in calculation or simulation of device characteristics. Preliminary experimental support is provided.