This is an extensive study of the non-aluminosilicate analogs of the zeolite RHO. This molecular sieve is of great interest commercially because of its catalytic properties. In the absence of rigid supporting structural subunits (smaller cages or channels), the aluminosilicate RHO exhibits atypical framework flexibility with large displacive rearrangements, The beryllophosphate and berylloarsenate analogs are easily synthesized under very mild reaction conditions and therefore may be of interest far inexpensive and rapid commercial production. However, they have decreased thermal stability. In an effort to increase thermal stability and explore framework flexibility, we have synthesized and characterized a series of analogs of the non-aluminosilicate RHO framework. All materials crystallize in the space group 123, ranging from a = 13.584(2) Angstrom for Li-BePO RHO to a = 14.224(4) Angstrom for Ba-RbBeAsO RHO for hydrated phases. The extra framework cations are distributed over the double 8-ring, single 8-ring, and two single 6-ring sites. Partially and fully dehydrated phases were also studied for changes in framework stability. Predictive trends based on the type of cation exchanged into the framework were determined by Be-9 and P-31 MAS NMR.