  According to the Erd\H{o}s-Szekeres theorem, for every $n$, a sufficiently
large set of points in general position in the plane contains $n$ in convex
position. In this note we investigate the line version of this result, that is,
we want to find $n$ lines in convex position in a sufficiently large set of
lines that are in general position. We prove almost matching upper and lower
bounds for the minimum size of the set of lines in general position that always
contains $n$ in convex position. This is quite unexpected, since in the case of
points, the best known bounds are very far from each other. We also establish
the dual versions of many variants and generalizations of the Erd\H os-Szekeres
theorem.
