Abstract. The notion of n-fold strong ideal in BH-algebra is in-troduced and some related properties of it are investigated. Therole of initial segments in BH-algebras is described. 1. IntroductionY. Imai and K. Iseki introduced two classes of abstract algebras:BCK-algebras and BCI-algebras ([2,3]). It is known that the class ofBCK-algebras is a proper subclass of the class of BCI-algebras. BCK-algebras have some connections with other areas: D. Mundici [5] provedMV-algebras are categorically equivalent to bounded commutative al-gebra, and J. Meng [6] proved that implicative commutative semigroupsare equivalent to a class of BCK-algebras. Y. B. Jun, E. H. Roh, and H.S. Kim [4] introduced the notion of a BH-algebra, which is a generaliza-tion of BCK=BCI-algebras. They de ned the notions of ideal, maximalideal and translation ideal and investigated some properties. E. H. Rohand S. Y. Kim [8] estimated the number of BH -subalgebras of order iin a transitive BH -algebras by using Hao’s method. S. S. Ahn and J.H. Lee ([1]) introduced the notion of strong ideals in BH-algebra andinvestigated some properties of it.In this paper, we introduce the notion of n-fold strong ideal in BH-algebra and investigated some related properties of it. We also describethe role of initial segments in BH-algebras.2. PreliminariesBy a BH-algebra ([4]), we mean an algebra (X;;0) of type (2,0)satisfying the following conditions:(I) xx = 0,(II) x0 = x,