In this paper we study som problems on the separability of k disjoint point sets in the plane. One one hand, we give algorithms for finding minimum cardinality separators by means of parallel lines or rays with common apex. On the other hand we show how to decide whether it is possible to separate by k-1 parallel lines, k rays with the same origin, an arrangement of 2-3 lines or, in the projective sense, by k lines through a point.