By a relational system we mean a couple (A, R) where A is a set and R is a binary relation on A, i.e. R ⊆ A × A. To every directed relational system A = (A, R) we assign a groupoid G(A) = (A, ·) on the same base set where xy = y if and only if (x, y) ∈ R. We characterize basic properties of R by means of identities satisfied by G(A) and show how homomorphisms between those groupoids are related to certain homomorphisms of relational systems.