Structurally　complicated　xi＇-　and　xi-phases　have　been　found,　for　the　first　time,　in　as-cast　Al73Ni5Rh22　and　Al75Ni15Rh10　alloys.　The　lattice　parameters　of　these　two　phases　were　determined　by　means　of　electron　diffraction　and　high-resolution　transmission　electron　microscopy　(　HREM).　These　two　phases　have　similar　orthorhombic　structures　but　with　different　lattice　parameters　of　a　=　23.2　angstrom,　b　=　16.4　angstrom,　c　=　12.0　angstrom　for　the　xi＇-phase　and　a　=　20.3　angstrom,　b　=　16.4　angstrom,　c　=　14.8　angstrom　for　the　xi＇-phase.　A　new　two-dimensional　domain-boundary　network　has　also　been　observed　in　these　two　phases.　Domain　boundaries　with　normals　closely　parallel　to　the　[001]　direction　are　actually　phason　planes　represented　by　a　translation　vector　of　r　=　(1/2)a　+　(1/2　tau)c　in　the　xi＇-phase　and　r　=　+/-(1/2　tau(2))　a　+　(tau/2)c　in　the　xi＇-phase,　whereas　the　newly-found　wide　and　zigzag　boundaries　perpendicular　to　the　above　set　were　attributed　from　the　step-like　boundary　structures　of　domains　related　by　a　translation　vector　of　r　=　(1/tau)((1/2)a　+　(1/2　tau)c).　The　structural　difference　between　the　two　types　of　planar　faults　is　discussed.