Additive manufacturing (AM) processes fabricate parts by adding material in a layer-bylayer fashion. In order to enable closed-loop process control-a major hurdle in the adoption of most AM processes-compact models suitable for control design and for describing the layer-by-layer material addition process are needed. This paper proposes a two-dimensional modeling framework whereby the deposition of the current layer is affected by both in-layer and layer-to-layer dynamics, both of which are driven by the state of the previous layer. The proposed framework can be used to describe phenomena observed in AM processes such as layer rippling and large defects in laser metal deposition (LMD) processes. Further, the proposed framework can be used to create twodimensional dynamic models for the analysis of layer-to-layer stability and as a foundation for the design of layer-to-layer controllers for AM processes. In the application to LMD, a two-dimensional linear-nonlinear-linear (LNL) repetitive process model is proposed that contains a linear dynamic component, which describes the dynamic evolution of the process from layer to layer, cascaded with a static nonlinear component cascaded with another linear dynamic component, which describes the dynamic evolution of the process within a given layer. A methodology, which leverages the two-dimensional LNL structure, for identifying the model process parameters is presented and validated with quantitative and qualitative experimental results.