Two design strategies are presented to create dual-band frequency selective surfaces based on multi-arm Archimedean spirals. A single-band element is first presented as the basis for the surface. The individual arm lengths of the spirals are utilised as the primary design parameter to synthesise the passband and stopband responses. The first approach uses a lattice of four-arm spirals with alternating sizes, and the second combines these into an eight-arm uniform lattice of elements. Measured and simulated results are included for a fabricated S-band prototype of each topology to demonstrate the basic design strategies. \ The Institution of Engineering and Technology 2015.