The paper describes an approach of exact linearization for multiinput power systems with nonlinear loads. The considered nonlinear differential algebraic systems (NDAS) are not in general state variable form. Some new definitions of M derivative and M bracket that are similar to the definitions of classic differential geometric theory and some related revised results are given. The definitions of M derivative and M bracket can be easily used to obtain the feedback control law of the NDAS. The conditions of exact feedback linearization are shown. When given NDAS satisfy the proper conditions of exact linearization

the multi-machine power systems with nonlinear loads can be transformed into Brunovsky standard form with constraint algebraic equations.