Abstract. Various characterizations of (m;n)-fold p-ideals of weak BCC-algebras are presented. 1. IntroductionBCC-algebras, introduced by Y. Komori (see [10] and [11]), are an algebraicmodel of BIK + -logic, i.e., implicational logic whose axioms scheme are theprincipal type-scheme of the combinators B, I, and K, and whose inferencerules are modus ponens and modus ponens 2, where p !q is inferred fromp !(r !q) and r. Several years later some authors introduced independentlymore extensive algebraic system using di erent names. This new algebraicsystems have the same partial order as BCC-algebras and BCK-algebras buthas no minimal element. Such obtained system is called a BZ-algebra [7, 15] ora weak BCC-algebra [2, 4, 13]. From the mathematical point of view the lastname is more corrected but more popular is the rst.Many mathematicians studied such algebras as BCI-algebras, B-algebras,di erence algebras, implication algebras, G-algebras, Hilbert algebras, d-algebrasand many others. All these algebras have one distinguished element and satisfysome common identities playing a crucial role in these algebras and, in fact, aregeneralization or a special case of weak BCC-algebras. So, results obtained forweak BCC-algebras are in some sense fundamental for these algebras, especiallyfor BCC/BCH/BCI/BCK-algebras.A very important role in the theory of such algebras plays ideals. Many typesof ideals in these algebras have been studied with various relations betweenthem (see for example [5] and [16]). In [14] X.H.Zhang, J.Hao and S.A. Bhattistudied p-ideals of BCI-algebras. In [8] Y.Huang and Z.Chen introduced thefoldness of some ideals in BCK-algebras. In [12] Kordi and Moussavi studied(m;n)-fold p-ideals and fuzzy (m;n)-fold p-ideals in BCI-algebras.This paper is a continuation of our study of p-ideals initiated in [5].