  A graph drawn in the plane with n vertices is k-fan-crossing free for k > 1
if there are no k+1 edges $g,e_1,...e_k$, such that $e_1,e_2,...e_k$ have a
common endpoint and $g$ crosses all $e_i$. We prove a tight bound of 4n-8 on
the maximum number of edges of a 2-fan-crossing free graph, and a tight 4n-9
bound for a straight-edge drawing. For k > 2, we prove an upper bound of
3(k-1)(n-2) edges. We also discuss generalizations to monotone graph
properties.
