  It is well known that the bidual of $\mathrm C(X)$ for a compact space $X$,
supplied with the Arens product, is isometrically isomorphic as a Banach
algebra to $\mathrm C(\tilde X)$ for some compact space $\tilde X$. The space
$\tilde X$ is unique up to homeomorphism. We establish a similar result for
realcompact spaces: The order bidual of $\mathrm C(X)$ for a realcompact space
$X$, when supplied with the Arens product, is isomorphic as an $f$-algebra to
$\mathrm C(\tilde X)$ for some realcompact space $\tilde X$. The space $\tilde
X$ is unique up to homeomorphism.
