  It has been proposed recently that the scale of quantum gravity (``the string
scale'') can be $M_S \sim$ few TeV with $n \geq 2$ extra dimensions of size $R
\stackrel{<}{\sim}$ mm so that, at distances greater than $R$, Newtonian
gravity with $M_{Pl} \sim 10^{18}$ GeV is reproduced if $M_{Pl}^2 \sim R^n
M_S^{n+2}$. Exchange of virtual gravitons in this theory generates
higher-dimensional operators involving SM fields, suppressed by powers of
$M_S$. We discuss constraints on this scenario from the contribution of these
operators to the processes $e^+ e^- \to W^+ W^-, ZZ, \gamma \gamma$. We find
that LEP2 can place a limit $M_S \approx 1$ TeV from $e^+ e^- \to W^+ W^-, ZZ,
\gamma \gamma$.
