Initial errors and model errors are the limiting factors to the improvement of the numerical weather prediction（NWP). Traditional NWP and variational data assimilation（VDA) always ignore the influence of model errors, but it is important to investigate the dynamics of model errors for deep research. Based on the nonlinear dynamic model, the model error equation and the mean quadratic error expression for short time which are independent of the particular model are obtained on the assumption that there exist model parameters error and physical processes lacking error in the prediction model, and the non-Markovian character of the probability density of the model error is proved with Liouville equation. Taking the Hopf bifurcating system and Lorenz low-order atmospheric systems as examples, the results indicate that the mean quadratic error is bound to behave like t2 in a short time; the mean quadratic error tends to a stable value after a long time; the parameters error is equivalent to the physical processes lacking error under certain condition. It will afford valuable information for the research of forecasting error correction and weak constraint VDA from the theoretic aspect.