The calculated trends of geometries and vibrational frequencies of several uranyl isoelectronic species, like the known NUN and CUO,and the unknown CUN-, NUO+, and NUF2+, are reported. The NUN and CUO results support the matrix spectroscopic assignments. The simplest example of equatorial coordination to uranyl is the C-2 nu species UO3. Its calculated vibrational frequencies also support matrix spectroscopic ones. We earlier suggested that the large range of uranyl bond lengths in UO66--type systems could be interpreted in terms of a "frozen, soft e(g) vibrational mode". Further studies on UF6, U(OH)(6), [(OUO)(F-eq)(n)]((n-2)-), [(OUO)(NO3)(3)](-), and [(OUO)(CO3)(3)](4-) show only small variation of R(ax) as function of R(eq). Thus, the all-oxide case is a special one, where all ligands are capable of single and multiple bonding.