steric configuration at 2-position carbon of N-protected-3- aminopropionic acid derivatives (3) to convert into the above substituted-3-amino-2-hydroxypropionic acid deriva› tives ( 4) in the coexistence of water from the beginning. 

[0088] Water is required to make the above by-products (8) responsible for the above impurity (9) harmless. The amount of water used is not limited to a particular range, and it is usually used in a molar amount above I-fold, preferably in a molar amount above 10-fold, more preferably in a molar amount above 20-fold, and most preferably in a molar amount above 50-fold, relative to the N-protected-3-amino› propionic acid derivatives (3). In general, as the amount of water used becomes larger, the effects become larger and duration required for treatment may be shortened. In this connection, from the viewpoint of productivity, water is usually used in a molar amount below 1000-fold, preferably in a molar amount below 500-fold, and more preferably in a molar amount below 100-fold, although there is no prob› lem even if a large amount of water is used. 

[0089] The temperature of the above heat treatment car› ried out in contact with water is not limited to a particular range if the temperature is below the boiling point of the reaction mixture. In general, as the temperature becomes higher, the effects by the contact with water become larger and duration required for treatment may be shortened. The treating temperature varies depending on various conditions such as the kind of substituted-3-amino-2-hydroxypropionic acid derivatives ( 4), the amount of water used, the contact duration with water, the acidity of a reaction mixture or the like, and can not be defined uniformly. The temperature may be preferably above 40° C., more preferably above 60° C., and most preferably above 80° C. 

[0090] The above contact with water is carried out under acidic to neutral conditions. In general, as the acidity becomes higher, the effects by the contact with water become larger and duration required for treatment may be shortened. The above contact is usually carried out under acidic to neutral conditions, preferably under acidic condi› tions, and more preferably under strongly acidic conditions. Also, a gradual shift from neutral to acidic conditions may be preferably carried out with the progress of the reaction. 

[0091] In the above contact with water, in order to main› tain the reaction under acidic to neutral conditions, prefer› ably under acidic conditions, and more preferably strongly acidic conditions and/or in order to shift the reaction to these conditions, if necessary, the reaction may be preferably carried out in the coexistence of an acidic substance. The acidic substance is not limited to a particular one. For example, organic acids include sulfonic acids such as meth› anesulfonic acid, ethanesulfonic acid, p-toluenesulfonic acid, o-, p- or m-nitrobenzenesulfonic acid; carboxylic acids such as formic acid, acetic acid, trifluoroacetic acid or benzoic acid, and inorganic acids include hydrochloric acid, sulfuric acid, sulfurous acid, phosphoric acid or the like. 

[0092] The amount of acidic substances used is not limited to a particular range, and they are usually used in a molar amount of0.01 to 100-fold, preferably in a molar amount of 0.05 to 50-fold, and more preferably in a molar amount of 0.1 to 20-fold, for example, relative to N-protected-3-ami› nopropionic acid derivatives (3). 

[0093] In this connection, if the acidity in the above contact with water is expressed using a pH value as an 

indicator (standard), the acidic to neutral conditions refer to usually a range below pH 9, preferably a range below pH 8, and more preferably a range below pH 7. Also, the acidic conditions refer to a range below pH 4 and the strongly acidic conditions refer to a range below pH 2. 

[0094] Next described is the third step wherein substi› tuted-3-amino-2-hydroxypropionic acid derivatives ( 4) are converted into 3-amino-2-hydroxypropionic acid deriva› tives (1 ). 

[0095] In this step, the substituents to be eliminated (sub› stituent S 4 on the oxygen atom of the carboxyl group, substituent S $^{5 }$on the oxygen atom at 2-position carbon, and substituent S $^{6 }$on the nitrogen atom at 3-position carbon) on the substituted-3-amino-2-hydroxypropionic acid deriva› tives ( 4) having an inverted steric configuration at 2-position carbon, which are obtained in the second step, are eliminated to convert into 3-amino-2-hydroxypropionic acid deriva› tives (1). If each of S 4 , S 5 and S 6 is a hydrogen atom, substituents to be eliminated are not present on each of oxygen and nitrogen atoms, of course. 

[0096] Methods for eliminating substituents to be elimi› nated are not limited to particular ones and include, for example, methods described in PROTECTIVE GROUPS IN ORGANIC SYNTHESIS, 2nd ed., JOHN WILLY & SONS pub!. (1991). Although preferable methods vary depending on the kind of protecting groups, they include, for example, acid treatment, base treatment, hydrolysis, catalytic reduc› tion, electrolytic reduction, Zn/AcOH treatment or the like. Among others, acid treatment or hydrolysis is convenient and generally used. In particular, hydrolysis is convenient and generally used. Hereinafter, a method by hydrolysis for eliminating the above substituents to be eliminated is spe› cifically described. 

[0097] In this step, the amount of water used for hydroly› sis is not limited to a particular range, and it is usually used in a molar amount above I-fold, preferably in a molar amount above 10-fold, more preferably in a molar amount above 20-fold, and most preferably in a molar amount above 50-fold, relative to substituted-3-amino-2-hydroxypropionic acid derivatives ( 4). Water may be used in an excess amount, also as a reaction solvent, and usually used so. In this connection, from the viewpoint of productivity, water is usually used in a molar amount below 1000-fold, preferably in a molar amount below 500-fold, and more preferably in a molar amount below 100-fold, although there is no prob› lem even if a large amount of water is used. If the treatment of contact with water is carried out in the above second step, water used in the treatment of contact with water may be used for hydrolysis in this step as it is, of course. 

[0098] In the above hydrolysis, various organic solvents usually used may coexist in a range not affecting the reaction, in addition to water used as reaction reagents. In general, the above substituted-3-amino-2-hydroxypropionic acid derivatives ( 4) have a tendency to dissolve hardly in water, and therefore, organic solvents having a high dissolu› bility may be used together for the purpose of promotion of the reaction, improvement of the property of the reaction solution or the like. Examples of the various organic sol› vents include aliphatic hydrocarbons such as hexane, hep› tane or methylcyclohexane; aromatic hydrocarbons such as toluene or xylene; halogenated hydrocarbons such as meth› ylene chloride or chloroform; ethers such as tetrahydrofuran, 

