Abstract Determination of the order of a model is the key first step towards modeling any dynamic systems, particularly two-dimensional processes. In this paper, a new method for two-dimensional (2-D) Gaussian ARMA model order determination is proposed. In the proposed method, the AR and MA orders are first independently determined, then the procedure for model order determination of the 2-D ARMA model is outlined. The model is assumed to be causal, stable, linear, and spatial shift-invariant with p 1 × p 2 quarter-plane (QP) support. Numerical simulations are presented to show the effectiveness of the proposed new approach.