The relation of alternativeness (accessibility) between elements of the set of possible worlds is the key concept of relational semantics. The model frame of this semantics has a large applicability in many kinds of non-classical logics. The paper analyses the concept of alternativeness in order to offer its philosophical elucidating. At the beginning an explanation of alternativeness in epistemic and temporal systems is presented. Then some positions on the question of ontological status of possible worlds are compared. In conclusion it is pointed out that the concept of alternativeness is a different way of formulating the idea of possibility.