Abstract: In this paper, the periodic boundary problem and the initial value problem for the nonlinear system of parabolic type u₁=-A(x, t)u_x4+B(x, t)u_x2+(g(u))_x2+(grad h(u))_x+f(u) are studied, where u(x, t)=(u₁(x, t).…, u_J(x, t) is a J-dimensional unknown vector valued function, f(u) and g(u) are the J-dimensional vector valued function of u(x, t), h(u) is a scalar function of u, A(x, t) and B(x, t) are J×J matrices of functions. The existent, uniqueness and regularities of the generalized global solution and classical global solution of the problems are proved. When J=1, h(u)=0, g(u)=au³, A=a₁, B=a₂, where a₁, a₂, a are constants, the system is a generalized diffusion model equation in population problem.