Quantum chemical calculations, using gradient-correct density functional at the BP86 level in conjunction with TZ2P basis sets, have been carried out for the radon hydrides HRnY (with Y = F, Cl, Br, I, CCH, CN, and NC). The bonding in HRnY is studied using different bond ruptures, establishing the role of those stabilizing (and destabilizing) factors that prevent these species to be dissociated. Although all HRnY systems studied here are bound equilibrium structures, they are metastable species with respect to the HRnY → Rn + HY decomposition channel. However, the HRnY → H + Rn + Y reaction is endothermic. So, these results indicate the possibility to identify the radon hydrides in noble-gas matrices.