According to the swiched complex mapping proposed by the author, the method constructing the switched processes generalized M (Mandelbrot) sets was elaborated, and a series of the switched processes generalized M sets for complex index number were constructed. The construction charaeteristies of the generalized M sets were expounded according to the analysis of teh algorithm constructing the generalized M sets. On the basis of what has already been achieved, the trajectories of a starting point in the complex C plane under the switched mapping were researched into, The results show the switched processes generalized M sets have the fractal feature, the construction characteristics of the switched processes generalized M sets are dependent on the complex number W and the switched variable ro, and the reaso which results in the discontinuity of switched processes generalized M sets is the discontinuity of choice of the pricipal range of phase angle.