We have computed the structure and stability of the xenon hydrides HXeY (with Y = F, Cl, Br, I, CCH, CN, NC) using relativistic density functional theory (DFT) at ZORA-BP86/TZ2P level. All model systems HXeY studied here are bound equilibrium structures, but they are also significantly destabilized with respect to Xe and HY. We have analyzed the bonding in HXeY in order to arrive at a simple picture that explains the main trends in stability.