We study the excited state absorption (ESA) properties of the four DNA bases (thymine, cytosine, adenine, and guanine) by different single reference quantum mechanical methods, i.e. equation of motion coupled cluster singles and doubles (EOM-CCSD), singles, doubles and perturbative triples (EOM-CC3), and time-dependent density functional theory (TD-DFT), with the long-range corrected CAM-B3LYP functional. Preliminary results at the Tamm-Dancoff (TDA) CAM-B3LYP level using the maximum overlap method (MOM) are reported for Thymine. In the gas phase, the three methods predict similar One Photon Absorption (OPA) spectra, which are also consistent with the experimental results and with the most accurate computational studies available in the literature. The ESA spectra are then computed for the pp states (one for pyrimidine, two for purines) associated with the lowest energy absorption band, and for the close-lying np state. The EOM-CC3, EOM-CCSD and CAM-B3LYP methods provide similar ESA spectral patterns, which are also in qualitative agreement with literature RASPT2 results. Once validated in the gas phase, TD-CAM-B3LYP has been used to compute the ESA in chloroform, including solvent effect by the polarizable continuum model (PCM). The predicted OPA and ESA spectra in chloroform are very similar to those in the gas phase, most of the bands shifting by less than 0.1 eV, with a small increase of the intensities and a moderate destabilization of the np state. Finally, ESA spectra have been computed from the minima of the lowest energy pp state, and are consistent with the available experimental transient absorption spectra of the nucleosides in solution, providing a final validation of our computational approach.