  In the paper we study pseudocompact primitive topological inverse semigroups.
We describe the structure of pseudocompact primitive topological inverse
semigroups and show that a Tychonoff product of a family of pseudocompact
primitive topological inverse semigroups is a pseudocompact topological space.
Also we prove that the Stone-\v{C}ech compactification of a pseudocompact
primitive topological inverse semigroup is a compact primitive topological
inverse semigroup.
