Abstract The direct method of calculating magnetic observables provided by the Liouville formalism is utilized for a nonperturbative numerical treatment of electron spin-echo-envelope modulation (ESEEM). Calculated time-domain signals are compared with experimental ones. The particular system studied is the C0 2 anion trapped in NaHC 2O 4·H 2O single crystals. The experimental ESEEM spectra show modulations due to both proton and sodium nuclei. The hyperfine and quadrupole tensors, determined independently by ENDOR spectroscopy, are used as input for calculating the ESEEM spectra.