This article treats absorption of electromagnetic waves by thin multilayer magnetogyrotropic structures. Two types of structures with uniaxial magnetic anistropy in each layer are proposed. In structure I, easy magnetization axes in layers are normal to the layers plane. In structure II, easy magnetization axes are parallel to one of the coordinate axes, lying in the layers plane. Structure I is made as glass-fiber-reinforced plastic, with each layer containing a set of tiles, made from textured hexaferrites. This structure can also be made from multilayer fabrics of ultrahigh molecular weight polyethylene fibers, filled with magnetically uniaxial hexaferrites, having natural ferromagnetic resonance frequencies from 14 to 40 GHz. Structure II is made as multilayer fabrics from ultrahigh molecular weight polyethylene fibers, filled with hexaferrites, having a plane or cone of magnetization and natural ferromagnetic resonance frequencies 1 to 20 GHz.