Two-dimensional adaptive filters are useful in a wide variety of image and video processing applications. Several different two-dimensional structures and algorithms have been developed, the most recent of which is a 2-D IIR adaptive filter. IIR adaptive filters offer reduced computational complexity and increased modeling flexibility when compared to FIR filters. A simple gradient algorithm is developed, and experimental results are presented which clearly show the dependence of convergence on the 2-D indexing scheme. Results show that the 2-D IIR mean-squared-error performance surface characteristics are similar to those of the 1-D IIR adaptive filter with respect to unimodality of the error surface. A quasi-Newton acceleration algorithm is suggested to improve the rate of convergence.