Cascading　similar　frequency　selective　surfaces　(FSSs)　improves　the　roll-off　rate　and　frequency　selectivity　of　THz　bandpass　filters.　However,　resonant　coupling　between　FSS　layers　causes　anomalous　transmission　peaks.　In　this　work,　we　have　employed　an　equivalent　circuit　model　to　analyze　a　double-layer　FSS　structure　with　periodic　cross　apertures　at　different　interlayer　spacing.　We　found　that　the　anomalous　peaks　can　be　attributed　to　the　resonant　coupling　between　the　upper　and　lower　layer　FSSs,　and　their　periodic　appearance　with　changing　interlayer　spacing　is　related　to　the　half-wavelength　repeatability　of　the　circuit.　We　have　fabricated　a　double-layer　FSS　sample　using　femtosecond　laser　micromachining　and　measured　it　using　time-domain　THz　spectroscopy.　The　results　using　the　equivalent　circuit　model　agree　with　the　Finite-Difference　Time-Domain　(FDTD)　and　experimental　results.　©　2020　by　the　authors.