High-harmonic spectroscopy probes atomic structure by looking at the short-wavelength emission excited from atoms by ultrafast pulses of laser light. It is now shown that this technique can even detect signatures of electron–electron interactions. High-harmonic spectroscopy provides a unique insight into the electronic structure of atoms and molecules1,2,3,4,5. Although attosecond science holds the promise of accessing the timescale of electron–electron interactions, until now, their signature has not been seen in high-harmonic spectroscopy. We have recorded high-harmonic spectra of atoms to beyond 160 eV, using a new, almost ideal laser source with a wavelength of 1.8 μm and a pulse duration of less than two optical cycles. We show that we can relate these spectra to differential photoionization cross-sections measured with synchrotron sources. In addition, we show that the high-harmonic spectra contain features due to collective multi-electron effects involving inner-shell electrons, in particular the giant resonance in xenon. We develop a new theoretical model based on the strong-field approximation and show that it is in agreement with the experimental observations.