A kind of the general finite difference schemes with intrinsicparallelism for the boundary value problem of the quasilinearparabolic system is studied without assuming heuristically thatthe original boundary value problem%for the quasilinear parabolic systemhas the unique smooth vector solution. By the method of a prioriestimation of the discrete solutions of the nonlinear differencesystems, and the interpolation formulas of the various norms ofthe discrete functions and the fixed-pointtechnique in finite dimensional Euclidean space, the existence anduniqueness of the discrete vector solutions of the nonlineardifference system with intrinsic parallelismare proved. Moreover the unconditional stability ofthe general finite difference schemes with intrinsic parallelismis justified in the sense of the continuous dependence of thediscrete vector solution of the difference schemes on the discretedata of the original problems in the discrete W(2,1)2 norms. Finally the convergence of the discrete vector solutions ofthe certain difference schemes with intrinsic parallelism to the unique generalized solution of the original quasilinear parabolic problem is proved.