This thesis details the study of nitrone cycloadditions to synthesize some novel isoxazolidines. Condensation of aldehydes A and B, with N-methylhydroxylamine led to the formation of nitrones. Cycloaddition of these nitrones gave a range of bicyclic isoxazolidine products. The cascade chemistry, involving condensation, cyclisation, and nitrone cycloaddition was utilised in the synthesis of the core structure found in iboga alkaloid natural products. Aldehydes C were synthesised and condensed with hydroxylamine to obtain a variety of isoquinuclidine cycloadducts. This cascade chemistry was used for the formal synthesis of 19-hydroxy-ibogamine. Starting with aldehyde C, X = Cl, R,R = S(CH2)3S, R1 = CH3 gave the cycloadduct D. This was converted to the amide E that represents the completion of the formal synthesis of this alkaloid. In addition, some studies were carried out towards an aldehyde needed for the cascade chemistry to investigate a proposed biosynthesis of the alkaloids daphlongeranines A and B.