A geometric space is a pair \((H,{\mathcal B})\), where \(H\) is a finite nonempty set (its elements are called points) and \(\mathcal B\) is a family of nonempty subsets of \(H\) (its elements are called blocks). If we put \({\mathcal B}=\{x\circ y\mid x,y\in H\}\) then \((H,{\mathcal B})\) is the geometric space associated to the hypergroupoid \((H,\circ)\). Two kinds of automorphisms of \((H,\circ)\) are considered, namely: (i) algebraic automorphisms (\(\varphi(x\circ y)=\varphi(x)\circ\varphi(y)\), for all \(x,y\) in \(H\)), (ii) geometric automorphisms (\(\varphi(B)\in{\mathcal B}\), for every \(B\in{\mathcal B}\)). The aim of this paper is to study connexions between the group of algebraic automorphisms \(\Aut_a(H,\circ)\) and the group of geometric automorphisms \(\Aut_g(H,\circ)\). Particularly, several such connexions corresponding to Steiner hypergroupoids are established.