A method for producing aromatic polyesters according to claim 2, wherein the compound A is a compound selected from the group consisting of p-hydroxybenzoic acid, m-hydroxybenzoic acid, m-hydroxybenzoic acid, 1-hydroxy-5-naphthoic acid, 2-hydroxy-6-naphthoic acid, 1-hydroxy-4-naphthoic acid and acylated or esterified compounds thereof, the compound B is a compound selected from the group consistin