High resolution Fourier transform spectra, recorded between 30 and 460 cm-1, have been used for an extensive analysis of the (n, τ) = (0, 3) ← (n', τ') = (0, 1), (0,1) ← (0, 3) and (1, 1) ← (0, 3) torsion-rotation bands of H2O2. Then, using a Hamiltonian which takes explicitly into account the strong |ΔKa| = 2 interaction between the rotational levels of the (n, τ) = (0,1) and (1,1) torsional states, as well as the |ΔKa| = 2 interaction between the (n, τ) = (1, 1) and (2, 1) rotational levels, it has been possible to reproduce very satisfactorily the experimental rotational levels of the (n, τ) = (0, 1) and (1,1) torsional states and a precise set of torsional energies and rotational and coupling constants has been derived. In the same way, to fit the (n, τ) = (0, 3) experimental energy levels we have used a Hamiltonian taking into account the |ΔKa| = 2 interaction between the rotational levels of the (n, τ) = (0, 3) and (1, 3) torsional states, and this calculation has also provided a precise set of torsional energies, rotational and coupling constants for the (n, τ) = (0, 3) and (1, 3) torsional states