This thesis deals with the synthesis of biologically active chiral bicyclic isoxazole and isoxazoline derivatives. The synthetic methodology involves two steps. In the first step, β-nitrostyrene derivatives were treated with allyl or propargyl malonates in the presence of chiral bifunctional thiourea catalyst to obtain the corresponding optically active Michael adducts. The resultant chiral Michael adducts were treated with DBU and 1,5-difluoro-2,4-dinitrobenzene (DFDNB) to generate nitrile oxides in situ. The nitrile oxide intermediates underwent intramolecular 1,3-dipolar cycloaddition with the neighboring dienophile to form chiral isoxazole and isoxazoline derivatives. In terms of yield and enatiomeric excess, this approach represents a highly efficient method for constructing the important class of molecules.