Covalent oligomeric and polymeric phases of SeO₂ and SO₂ have been investigated at high levels of density functional calculations on molecular and periodic models. Polysulfite [–S(O)O–]_x, a one-dimensional allotropic form of SO₂, is calculated to be energetically less stable than free molecular sulfur dioxide by less than 11 kcal mol⁻¹. This small energy difference δE renders polysulfite a candidate for experimental investigation. Its valence isoelectronic analog, the crystalline downeyite phase with linear [–Se(O)O–]_x chains, is more stable than the molecular species SeO₂ by 20 kcal mol⁻¹. Substituting sulfur for selenium in the one-dimensional [–Se(O)O–]_x structure containing sp³ chalcogen atoms slightly favors the 18-valence electron triatomic species. This feature may be related to the s–p energy difference, which diminishes on going down group 16. Finite molecular aggregates such as the four-membered rings X₂O₄ (X = S, Se; C_2v and C_2h symmetry) and S₄O₈ (D_4h) are also investigated at the B3LYP level using extended basis sets.