The HO(3) and HO(4) polyoxide radicals have attracted some attention due to their potential role in ozone chemistry. Experimentally, the geometrical structure of HO(3) is known whereas that of HO(4) is not. Moreover, the existence of the latter radical has been questioned. Theoretical calculations on the two species have been reported before, showing important structural differences depending on the computational level. Both radicals present an unusually long OO bond (around 1.7-1.8 A) that can be associated with an intricate interaction between HO, or HO(2), with O(2). The nature of such interaction is investigated in detail using large scale ab initio methods (CASSCF, CASPT2, MRCI, QCISD, CCSD(T)) and density functional techniques (B3LYP) in connection with extended basis sets. Stabilization enthalpies at 298 K with respect to HO (or HO(2)) and O(2) have been computed amounting to -3.21 kcal mol(-1) for HO(3) (trans conformation) and 11.33 kcal mol(-1) for HO(4) (cis conformation). The corresponding formation enthalpies are 6.12 and 11.83 kcal mol(-1). The trans conformation of HO(4) is less stable than the cis one by 6.17 kcal mol(-1). Transition states for HO(4) dissociation and for cis/trans conversion are also described.