In this paper, we investigae convergence behaviors of a differential method for 2-D motion parameter estimation. While the differential method is widely studied for motion compensated prediction in video coding, little attention hs been paid to its convergence properties. Based on the nonseparable exponential covariance image model, we derive the estimates of update terms for the 2- and 6-parameter motion models. And, the effect of noise, spatial correlation, choice of spatial gradient measures, andthe size of a region, are quantitatively anlyzed in relation to the convergence speed. Some empirical results are presented to verify the analysis.