We have theoretically investigated the correlation satellite spectra associated with the single-site (ss) and two-site (ts) double core-hole (DCH) states. The calculated ssDCH satellite spectra of N-2 (N 1s(2)) and CO (O 1s(2)) reproduced the observed experimental spectra satisfactorily and provided the first detailed assignments. DCH spectroscopy using X-ray two-photon photoelectron spectroscopy (XTPPS) was examined taking account of the single core-hole (SCH) and DCH satellite spectra. The results demonstrate that in XTPPS the ssDCH satellite spectrum is separated from other SCH/tsDCH spectra, while the tsDCH states and their satellite states may be overlapped with the SCH satellite spectrum. (C) 2011 Elsevier B. V. All rights reserved.