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(4a), or by substitution of an alkoxy group (-OR 4 ) of an alkoxycarbonyl group (-COOR 4 ) of the above N-alkoxy› carbonyl-3-amino-2-hydroxypropionic acid derivative ( 4b) with a 2-position hydroxyl group in the same molecule. In this connection, the oxazolidinone derivative ( 4c) can be formed whether water coexists in this step or not. 

[0063] In the substituted-3-amino-2-hydroxypropionic acid derivatives (4) obtained in this step, S 4 (or S 7 , S $^{8 }$or S9 ) represents a hydrogen atom or an ester residue. The above ester residue represents a monovalent organic group which can serve as an ester-type protecting group for a carboxyl group, for example, by being included in a structure repre› sented by ----COOS 4 or the like. The above monovalent organic group is not limited to a particular one if it has an effect of protecting the carboxyl group, and may be selecter from the ester-type protecting groups as described, for example, in PROTECTIVE GROUPS IN ORGANIC SYN› THESIS, 2nd ed., JOHN WILLY & SONS pub!. (1991). Among others, a lower alkyl group having 1 to 4 carbon atoms or a substituted or unsubstituted benzyl group is preferably used. A lower alkyl group having 1 to 4 carbon atoms is more preferably used and a methyl group or an ethyl group is further preferably used. A methyl group is most preferably used. 

[0064] S 3 in the N-protected-3-aminopropionic acid derivatives (3) and S 4 (or S 7 , S 8 or S 9 ) in the substituted-3- amino-2-hydroxypropionic acid derivatives (4) may be the same. 

[0065] It is simple and convenient if they are the same, and generally, they are often the same. However, they may be converted by esterification, hydrolysis, transesterification or the like under the conditions of this reaction. Furthermore, it necessary, known esterification, hydrolysis, transesterifi› cation or the like may be introduced into this step, and they may be freely selected in a range of not affecting the step. For example, if S 3 is an ester residue in the 3-aminopropi› onic acid derivatives (3), for example, this reaction may be preferably carried out in the presence of water ( or using water as a reaction solvent), and if necessary, the ester site may be hydrolyzed, to derive substituted-3-amino-2-hy› droxypropionic acid derivatives ( 4) wherein S $^{4 }$is a hydrogen atom. 

[0066] Next, reaction conditions of the second step are described. 

[0067] Preferably, this reaction is carried out under heat› ing. The reaction temperature is not limited to a particular range if it is below the boiling point of the reaction mixture. It may be preferably above 40° C., more preferably above 60° C., and most preferably above 80° C. In general, as the temperature becomes higher, the reaction proceeds more rapidly. 

[0068] Also, in this step, an acid treatment or abase treatment may be carried out for the purpose of promoting the reaction, if necessary, by coexistence or addition of a suitable amount of an acidic substance or a basic substance as a reaction accelerator. This treatment allows the reaction to proceed repidly at a lower temperature, and therefore, it is possible to carry out the inversion step at a milder treating temperature or a far milder treating temperature. The treat› ing temperature in this case is usually below about 40° C., and it is also possible to carry out the step at a temperature 

below about 20° C. It is particularly preferable to carry out the step in the coexistence of an acidic substance, because it has a high effect of promoting the reaction and it allows a later water treatment step to be carried out easily under an acidic to neutral condition. 

[0069] The acidic substance is not limited to a particular one. Organic acids include, for example, sulfonic acids such as methanesulfonic acid, ethanesulfonic acid, p-toluene› sulfonic acid, o-, p- or m-nitrobenzenesulfonic acid; car› boxylic acids such as formic acid, acetic acid, trifluoroacetic acid or benzoic acid. Inorganic acids include, for example, hydrochloric acid, sulfuric acid, sulfurous acid, phosphoric acid or the like. Also, in this reaction, leaving group L is eliminated to produce secondarily a conjugate acid of the leaving group L represented by the following general for› mula (7): 

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[0070] wherein L is as defined above, 

and the conjugate acid (7) of the leaving group Lis also used as an acidic substance preferably. 

[0071] 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 the N-protected-3- aminopropionic acid derivatives (3). 

[0072] Also, the basic substance is not limited to a par› ticular one, and weakly basic substances are preferably used. The weakly basic substances are not limited to particular ones. In general, basic substances showing a pKa value below 10, for example, of the conjugate acid in an aqueous solution are preferably used, and especially, those showing a pKa value below 5 are more preferably used. Specific examples include, for example, amines such as triethy› lamine, diisopropylamine or pyridine; carbonates such as sodium carbonate or potassium carbonate; hydrogen carbon› ates such as sodium hydrogencarbonate or potassium hydro› gencarbonate. Organic solvents showing a weak basicity such as N,N-dimethyl formamide, dimethyl sulfoxide or the like are also within a range of selection. 

[0073] The amount of the basic substances used is not limited to a particular range, and they are usually used in a molar amount of 0.01 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 the N-protected-3-aminopropionic acid derivatives (3). 

[0074] In general, acidic substances are preferably used as the above reaction accelerator, bacause they are easily removed from the reaction mixture after completion of the reaction and they have small influence in the yield and quality of the products even if they are brought in the next step as they are. 

[0075] Reaction solvents used in this reaction are not limited to particular ones, and various solvents usually used may be used. Examples of the reaction solvents include, for example, aliphatic hydrocarbons such as hexane, heptane or methylcyclohexane; aromatic hydrocarbons such as toluene or xylene; halogenated hydrocarbons such as methylene chloride or chloroform; ethers such as tetrahydrofuran, 1,4- dioxane or t-butyl methyl ether; aliphatic acid esters such as 

