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. $R\subseteq A\times A$. To every directed relational system $𝒜=(A,R)$ we assign a groupoid $𝒢\left(𝒜\right)=(A,·)$ on the same base set where $xy=y$ if and only if $(x,y)\in R$. We characterize basic properties of $R$ by means of identities satisfied by $𝒢\left(𝒜\right)$ and show how homomorphisms between those groupoids are related to certain homomorphisms of relational systems.