The synthesis and conformational analysis of a new type of conformationally restricted alpha-amino acid analogue of the amino acid antibiotic furanomycin is presented. The restriction involves the cis-fused cyclobutane and tetrahydrofuran units, generating the unusual 2-oxabicyclo[3.2.0]heptane core, which is found in a great number of biologically active natural products. The synthetic strategy is based on a formal [2 + 2] cycloaddition between 2-(acylamino)acrylates as acceptor alkenes and 2,3-dihydrofuran as a donor alkene, promoted by bulky aluminum-derived Lewis acids, particularly by methylaluminoxane (MAO). Additionally, following the same strategy, the synthesis of furanomycin analogues incorporating the 2-oxabicyclo[4.2.0]octane is reported.