Ahstract-In this paper, the problem of model reduction for two-dimensional (2-D) systems in the Fornasini-Marchesini local state-space form is addressed by matching zero-order moments. Two characterizations of zero-order moments are proposed: the first based on the notion of interpolation of complex points and the second based on the concept of steady state. A parameterized family of reduced-order models that achieves moment matching while preserving the 2-D structure of the original system is presented. The developed theory is illustrated by means of a 2-D low-pass filter reduction problem.