Let S be a subset of a metric space X and let B ( X ) be the class of all nonempty bounded subsets of X with the Hausdorff pseudometric H . A mapping F : S → B ( X ) is a directional contraction iff there exists a real α ∈ [ 0 , 1 ) such that for each x ∈ S and y ∈ F ( x ) , H ( F ( x ) , F ( z ) ) ≤ α d ( x , z ) for each z ∈ [ x , y ] ∩ S , where [ x , y ] = { z ∈ X : d ( x , z ) + d ( z , y ) = d ( x , y ) } . In this paper, sufficient conditions are given under which such mappings have a fixed point.