PURPOSE: To obtain a dyed fabric having clear and highly reproducible dyed color even by HT dyeing process with a dyeing bath having a pH adjusted to alkaline side by dyeing a polyester fiber with a specific monoazo disperse dye.

CONSTITUTION: A polyester or a polyester-containing fiber structure is dyed with a monoazo disperse dye expressed by formula (X is 1-6C alkyl, cyclopentyl, cyclohexyl, 1-4C alkoxy, H, F, Cl, Br or trifluoromethyl; Y is H, methyl, l-4C alkoxy, Cl or unsubstituted or 1-4C alkoxy-substituted-(1-5C) alkylcarbonylamino; R1 is H, 1-6C linear or primary branched alkyl, allyl, cyanoethyl, etc.; R2 is 1-6C linear or primary branched alkyl, allyl, cyclopentyl, etc.). An HT dyeing can be carried out in high reproducibility by adjusting the pH of the bathing bath to 8-10. The dyeing bath is preferably incorporated with a buffering substance such as acetic acid/pyrophosphoric acid salt.