The canonical equations of Hamilton-Tabarrok-Leech and Raitzin-Tabarrok-Leech for generalized nonconservative systems were established respectively. Three kinds of the principles of new form least action for generalized nonconservative systems were given, namely, the principles of new form least action of Lagrange-Tabarrok-Leech, the principles of new form least action of Raitzin-Tabarrok-Leech and the principles of new form least action of Lagrange-Raitzin-Tabarrok-Leech. And two examples were given to illustrate the application of the results.