In this paper, the nonstationary (time-dependent) boundary layer system (TDBLS) in Newtonian and Non-Newtonian flows is studied. There are some open problems in this field (see [1]). Using the method of parabolic regularization, the global existence of the weak solutions of TDBLS for the pseudo-plastic fluids is proved. The local existence of the weak solutions of TDBLS for the dilatable fluids is established. Finally, the uniqueness and stability of the weak solutions is discussed.