In this (essentially self-contained) paper the author continues his earlier investigations on demi-p-lattices [J. Symb. Logic 52, 712-724 (1987; Zbl 0628.06011)]. In Section 2, definitions and some new characterizations of demi-p-lattices, almost p-lattices and p-lattices are presented. Main results of this paper are to characterize the principal congruences on demi-p-lattices, which extends the corresponding characterization for p-lattices [\textit{H. Lakser}, Proc. Am. Math. Soc. 37, 32-36 (1973; Zbl 0269.06005)]. As an application of this characterization it is shown that the variety of demi-p-lattices has equationally definable principal congruences - a result which strengthens an earlier result that this variety has the congruence extension property. Section 4 describes a construction of a class of subdirectly irreducible demi-p-lattices and Section 5 uses this construction and the characterization of principal congruences (obtained in Section 3) to characterize the subdirectly irreducible demi-p-lattices, thus giving a partial solution to one of the problems raised in the author's earlier paper [loc. cit.]. This characterization extends the corresponding result of Lakser [loc. cit.] which was proved for p-lattices.