The　atomic　structures　of　four　structurally　complex　phases　of　an　Al-Pd-Mn　alloy,　namely　the　Psi-,　xi(1)-,　xi(2)-　and　xi　3-phases,　have　been　determined　by　means　of　high-resolution　electron　microscopy　and　by　theoretical　structure　simulations　based　on　the　periodic　stacking　of　two　different　types　of　phason　planes.　The　structural　characteristics　of　the　Psi-phase　appears　as　a　thin　slab　of　xi＇-phase　sandwiched　between　a　pair　of　type-1　phason　planes;　in　addition,　three　newly-found　xi(i)-phases　(i　=　1-3)　were　constructed　by　periodic　stacking　of　the　type-2　phason　planes　with　an　adjacent　stacking　(xi(1)),　centred　by　a　flattened　hexagon　(xi(2)),　which　are　sandwiched　around　a　thin　slab　of　xi-phase　(xi(3)).　High-resolution　electron　microscopy　image　simulations　of　the　Psi-phase　based　on　our　structural　model　match　very　well　with　the　experimental　results　and　this　agreement　is　also　supported　by　electron　diffraction　and　X-ray　powder　diffraction　simulations　based　on　the　model.　Our　results　show　that　structural　models　of　periodic　stacking　of　two　types　of　phason　planes　can　be　used　to　construct　the　atomic　structure　of　xi＇-　and　xi-phase　related　superstructures　in　the　Al-Pd-Mn　alloy.