Salinosporamide A, a potent proteasome inhibitor isolated from actinomycete bacteria Salinospora tropica, has attracted much attention in the chemical and biological communities due to its intriguing molecular architecture as well as characteristic biological properties. We envisaged Conia-ene type reaction of a 2-(but-3-ynamido)malonate for the construction of its γ-lactam core. Although there was no precedent for the synthesis of γ-lactams by Conia-ene reaction, we found that Ni(acac)_2-Yb(OTf)_3 and In(OTf)_3 promoted cyclization of 12 to 13 in good yields, respectively. Moreover, we also found that SiO2 effected this conversion in excellent yield although the reaction was rather slow. It should be stressed that each of these conditions did not cause any substantial racemization as well as isomerization of the exo olefin of 13. Lactam 13, thus prepared, was stereoselectively converted to Corey's intermediate 21 via selenoacetalization giving 17, discrimination of the two esters giving 19, cyclohexynylation giving 20, and deprotection. Following the Corey's procedure, we achieved a total synthesis of salinosporamide A. Neooxazolomycin, a potent antitumor antibiotic isolated from Streptomyces strains, was also synthesized by a convergent strategy that features a highly stereoselective approach involving the above-mentioned Conia-ene type cyclization, dihydroxylation accompanied by lactonization, and Nozaki-Hiyama-Kishi reaction to construct right hand segment 29 and an improved assembly of left hand segment 30. In the key Conia-ene type cyclization of 26 to 27, Ni(acac)_2-Yb(OTf)_3 and In(OTf)_3 turned out to effect this conversion in complete E-selectivity, while SiO_2 did not cause this cyclization at all.