Abstract Oil palm empty fruit bunches (EFB) are a lignocellulosic by product generated by palm oil mills. Delignified EFB fiber is a potential source of inexpensive hemicellulose, a substrate that is easily hydrolyzed to sugars for use in diverse biotechnological processes. The conditions for maximized selective removal of lignin from EFB fiber via separate treatments with alkaline peroxide and peracetic acid, were established such that the loss of hemicellulose was kept to a minimum. The amount of a reagent used in delignification, the temperature and the length of treatment, were optimized using a combination of Box–Behnken experimental design and the response surface method. Treatments with peracetic acid always left behind more hemicellulose and removed more lignin compared with the treatments involving alkaline peroxide. Under the best conditions (20 cm3 peracetic acid per g EFB, 35 °C, reaction time of 9 h), hemicellulose, cellulose and acid insoluble lignin constituted (dry weight basis) nearly 36%, 47% and ∼16%, respectively, of the treated acetone-washed extractive-free EFB fiber. Approximately 53% of the lignin was removed, but nearly all the hemicellulose was retained.