The results of experimental studies of a coaxial free-electron masers (FEM) based on two-dimensional distributed feedback are presented. In the first set of experiments the FEM's interaction region was formed by a two-mirror cavity with 2D Bragg structures as input and output mirrors. In the second set of experiments a cavity with 2D and 1D mirrors was used. In both cases the input mirror provided two-dimensional (2D) distributed feedback and ensured mode selection over the wave azimuthal index, while the output mirror was used to close the feedback loop inside the two-mirror cavity. It was demonstrated that substituting the 2D output mirror with a 1D Bragg structure increased the output power while still maintaining spectral purity and spa...