We give a detailed account of the Algebraically Closed and Existentially Closed members of the second Lee class B 2 of distributive p-algebras, culminating in an explicit construction of the countable homogeneous universal model of B 2. The axioms of Schmid [7], [8] for the AC and EC members of B 2 are reduced to what we prove to be an irredundant set of axioms. The central tools used in this study are the strong duality of Clark and Davey [3] (...) for B 2 and the method of Clark [2] for constructing AC and EC algebras using a strong duality. Applied to B 2, this method transfers the entire discussion into an equivalent dual category X 2 of Boolean spaces which carry a pair of tightly interacting orderings. The doubly ordered spaces of X 2 prove to be much more readily constructed and analyzed than the corresponding algebras in B 2. (shrink)