To investigate the mechanism of the electrochemical insertion of lithium into the CoO electrode in a Li/Li-y-CoO cell, we applied a two-dimensional (2D) correlation analysis to the spectra of the LiyCoO system during the first insertion-extraction reaction as obtained by lithium concentration-dependent X-ray absorption spectroscopy (XAS) and Raman spectroscopy. 2D XAS and 2D Raman spectra yield great resolution enhancement and show that the insertion of lithium into the CoO electrode leads to Li2O formation. Moreover, by analyzing the sign of the asynchronous cross peaks, we reveal the sequence of the first insertion process: first, the intensity of the band due to CoO decreases and then that of the band due to Li2O increases. A 2D heterospectral XAS-Raman correlation analysis was also undertaken of the same XAS and Raman spectra. This heterospectral 2D correlation analysis has elucidated not only the sequence of events between XAS and Raman signals from the same species but also the correlation between the XAS and Raman bands, confirming their band assignments.