  In this paper we enumerate $k$-noncrossing tangled-diagrams. A
tangled-diagram is a labeled graph whose vertices are $1,...,n$ have degree
$\le 2$, and are arranged in increasing order in a horizontal line. Its arcs
are drawn in the upper halfplane with a particular notion of crossings and
nestings. Our main result is the asymptotic formula for the number of
$k$-noncrossing tangled-diagrams $T_{k}(n) \sim c_k n^{-((k-1)^2+(k-1)/2)}
(4(k-1)^2+2(k-1)+1)^n$ for some $c_k>0$.
