  After simultaneous compactification of spacetime and worldvolume on $K3$, the
$D=10$ heterotic fivebrane with gauge group $SO(32)$ behaves like a $D=6$
heterotic string with gauge group $SO(28) \times SU(2)$, but with Kac--Moody
levels different from those of the fundamental string. Thus the
string/fivebrane duality conjecture in $D=10$ gets replaced by a string/string
duality conjecture in $D=6$. Since $D=6$ strings are better understood than
$D=10$ fivebranes, this provides a more reliable laboratory in which to test
the conjecture. According to string/string duality, the Green--Schwarz
factorization of the $D=6$ spacetime anomaly polynomial $I_{8}$ into $X_4\,
\tilde{X}_4$ means that just as $X_4$ is the $\sigma$-model anomaly polynomial
of the fundamental string worldsheet so $\tilde{X}_4$ should be the
corresponding polynomial of the dual string worldsheet. To test this idea we
perform a classical dual string calculation of $\tilde{X}_4$ and find agreement
with the quantum fundamental string result. This also provides an {\it a
posteriori} justification for assumptions made in a previous paper on
string/fivebrane duality. Finally we speculate on the relevance of
string/string duality to the vacuum degeneracy problem.
