The thermodynamics and the dynamics of incompatible polydisperse polymer blends are analyzed. The free energy is constructed following the Flory-Huggins approach, where the degree of incompatibility is characterized by the Flory interaction parameter chi. The Cahn-Hillard approximation is used to analyze the early stages of spinodal decomposition dynamics of a polymer blend quenched into the unstable region. A blend of polydisperse A polymers with the Schulz-Flory distribution and monodisperse B polymers is analyzed by treating polymer A as a one-, two-, and three-component system with a weight-average degree of polymerization and a polydispersity index, which we refer to as two-, three-, and four-component models, respectively. The thermodynamics and the dynamics of incompatible monodisperse A-monodisperse B polymer blends are consistent no matter which model is used. When polymer A is polydisperse, however, [S(k,t) - S(k,0)]/S(k,0), where S(k,t) is the characteristic structure function, is definitely different in the three different models due to kinetic effects. The differences are dependent on the functional form of the Onsager coefficients. For wavevector-independent Onsager coefficients, the reduced wavevector for which [S(k,t) - S(k,0)]/S(k,0) is a maximum, k(peak)* is always equal to 1/square-root 2 in the two-component model, while k(peak)* increases as x increases in the three- and four-component models. While for wavevector-dependent Onsager coefficients, k(peak)* decreases as chi increases in the three different component models. As chi --> infinity, the difference in k(peak)* between two- and three-component models and between three- and four-component models is 0.05 and 0.02, respectively, independent of the weight-average degree of polymerization when the polydispersity index of polymer A is equal to 2.0. When the polydispersity index of polymer A is reduced to 1.5, the difference in k(peak)* becomes 0.04 and 0.01, respectively.