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This paper presents a boundary integral formulation to analyze multilayered doubly-periodic lossy structures with arbitrary geometry. The formulation is based on the moment method using first-order triangular patch basis functions. Each individual layer is analyzed separately using the simple free-space Green's function. After discretization, periodic boundary conditions are imposed on each region and a connection scheme is used to connect the regions. Metallic patches between layers or on the periodic boundary are also included in the model. Several examples are presented showing both the flexibility and the accuracy of the method.