The six-dimensional torsion-vibration Hamiltonian of the H2O2 molecule and its H/D- and 18O/16O-isotopomers is derived. The Hamiltonian includes the kinetic energy operator, which depends on the tunneling coordinate, and the potential energy surface represented as a quartic polynomial with respect to the small-amplitude transverse coordinates. Parameters of the Hamiltonian were obtained from DFT calculations of the equilibrium geometries, eigenvectors, and eigenfrequencies of normal vibrations at the stationary points corresponding to the ground state and both the cis- and trans-transition states, carried out with the B3LYP density functional and 6-311+G(2d,p) basis set. The quantum dynamics problem is solved using the perturbative instanton approach generalized for the excited states situated above the barrier top. Vibration-tunneling spectra are calculated for the ground state and low-lying excited states with energies below 2000 cm–1. Strong kinematic and squeezed potential couplings between the large-amplitude torsional motion and bending modes are shown to be responsible for the vibration-assisted tunneling and for the dependence of tunneling splittings on the quantum numbers of small-amplitude transverse vibrations. Mode-specific isotope effects are predicted.