In this paper another class of Dark Matter candidate particles — the pseudoscalar and scalar light bosonic candidates — is discussed. Particular care is devoted to the study of the processes for their detection (which only involves electrons and photons/X-rays) in a suitable underground experimental setup. For this purpose the needed calculations are developed and various related aspects and phenomenologies are discussed. In particular, it is shown that — in addition to the WIMP cases already discussed elsewhere — there is also possibility for a bosonic candidate to account for the 6.3σ C.L. model independent evidence for the presence of a particle DM component in the galactic halo observed by DAMA/ NaI . Allowed regions in these scenarios are presented also paying particular care on the cosmological interest of the bosonic candidate.