Resonances between core-hole states have been long hypothesized to understand nonlinear responses of atoms and molecules exposed to intense x-ray free-electron laser (XFEL) pulses, but evaded clear identification in previous studies due to their transient nature. Here we report clear evidence of core-to-core resonances by state-of-the-art electron-ion coincidence spectroscopy on Kr atoms. The observed $3p\text{−}3d$ resonance manifested the significance in multiple ionization to highly charged states against the ultrafast core-hole decay. The present study, elucidating the role of the core-to-core resonance in electronic responses of matter to high-frequency laser fields, will advance our understanding of nonlinear spectroscopy and ultrafast imaging by ultrashort intense EUV and x-ray pulses.

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• Atomic & molecular processes in external fields
• Autoionization & Auger processes
• Multiphoton or tunneling ionization & excitation
• Single- and few-photon ionization & excitation
• Free-electron lasers
• Inner-shell processes
• Photoionization
• Ultraviolet photoelectron spectroscopy