Virtual knot theory, introduced by L. Kauffman, is a generalization
of classical knot theory. It naturally yields the notion of
a virtual braid, which is closely related to the notion of
a welded braid due to R. Fenn, R. Rimányi and C. Rourke.
In this paper we prove that any virtual link or welded link
can be described as the closure of a virtual braid or welded
braid, respectively, which is unique up to certain basic moves.
This is analogous to the Alexander and Markov theorems for
classical braids and links.