Calculations of high-order above-threshold-ionization (ATI) spectra for a zero-range model potential are interpreted in terms of quantum orbits as they formally result from a saddle-point evaluation of the S-matrix element. The spectrum is built up by the superposition of these orbits and exhibits distinctive interference patterns. For a laser with elliptical polarization, the ATI plateau becomes a stair whose individual steps can be attributed to particular quantum orbits. The real parts of the orbits are depicted. They are closely related to electronic space-time orbits. For parameters around an ATI channel closing, the spectrum shows resonant behavior.