We consider the possibility of several mechanisms contributing to the ββ0ν decay amplitude in the general case of CP non-conservation: light Majorana neutrino exchange, heavy left-handed (LH) and right-handed (RH) Majorana neutrino exchanges, lepton charge non-conserving coupling in SUSY theories with R_p breaking. We study the cases of two “non-interfering” and two “interfering” mechanisms and we show how the lepton-number-violating parameters characterizing each of the considered mechanisms can be determined from data on the ββ0ν decay half-lives of two or three nuclear isotopes, respectively. This method can be generalized to the case of more than two ββ0ν decay mechanisms and allows to treat the cases of CP-conserving and CP–non-conserving couplings generating the ββ0ν decay in a unique way.