A design of a chiral ligand and its metal-coordinated catalyst is very important for achievement of a highly optical purity and a chemical yield in an asymmetric reaction. Recently, we developed the chiral oxazolidine ligands having N,O-acetal structure, such as phosphinooxazolidine (POZ), phosphinooxazinane (POZI) and oxazolidine (OZ). POZ and POZI afforded products in an excellent enantioselectivities in Pd-catalyzed asymmetric allylic alkylation and tandem allylation. Furthermore, cationic Pd-POZ catalysts showed high levels of catalytic activity in the asymmetric Diels-Alder (DA) reactions of some dienes with oxazolidinone or pyrrazolidinone typed dienophiles. Cationic Pd-POZ catalyst showed an excellent catalytic activity in the DA reaction in ionic liquid (IL). The catalyst could be reused eight times without significant decrease of yield and enantioselectivity in the use of an ionic liquid as a solvent. OZ ligand also worked as organocatalyst in the DA reaction of 1,2-dihydropyridines with acroleins to afford the useful intermediate of Tamiflu. The review summarizes these our studies.