Let P be a topological property. A space X is said to be star P if whenever U is an open cover of X, there exists a subspace A ⊆ X with property P such that X = St(A,U), where St(A, U) = ∪ {U ∈ U : U ∩A ≠ ∅}. In this paper, we study the relationships of star P properties for P ∈ {Lindelöf, compact, countably compact} in pseudocompact spaces by giving some examples.