The structure of xenon adsorbed on the Cu(110) surface was determined in a combined experimental and theoretical study. The experimental results were obtained using helium-atom diffraction. In the entire temperature and coverage regime studied (20 K T s 170 K and Θ < 1 monolayer) the xenon adlayer can be described in terms of (n 2) high-order commensurate (HOC) structures, with n ≥ 7. As a result of the weak commensurability along the [110] direction, a series of uniaxial first-order phase transitions between (n 2) structures with different n is observed as a function of coverage and annealing temperature. In most cases these transitions are not completely reversible, indicating that the apparent stability of some of the HOC phases might be due to kinetic limitations, i.e. an effective @'pinning@' of the adlayer by the substrate. Along the highly corrugated [001] direction, the adlayer is in perfect registry with the substrate lattice. Inside the (n 2) unit cell, the xenon atoms form a quasi-hexagonal array. The experimental data were compared to the minimum free-energy configurations of the xenon adlayer calculated for surface temperatures between 0 and 75 K. These calculations are based on parameterized interaction potentials fitted to the measured thermodynamic properties of xenon on Cu(110). The experimental results, in particular the stability of the various HOC phases and their sequence with temperature, is well reproduced by the calculations assuming a corrugation of the holding potential along the [110] direction of about 4 meV. The energy difference between the most stable HOC structures is found to be quite small, in agreement with the observed @'metastability@' of the structures. The calculations further reveal that the details of the sequence and the temperature range of stability of the HOC phases strongly depends on the corrugation and the exact lattice misfit.