  Symplectic torus bundles $\xi:T^{2}\to E\to B$ are classified by the second
cohomology group of $B$ with local coefficients $H_{1}(T^{2})$. For $B$ a
compact, orientable surface, the main theorem of this paper gives a necessary
and sufficient condition on the cohomology class corresponding to $\xi$ for $E$
to admit a symplectic structure compatible with the symplectic bundle structure
of $\xi$ : namely, that it be a torsion class. The proof is based on a
group-extension-theoretic construction of J. Huebschmann (Sur les premieres
differentielles de la suite spectrale cohomologique d'une extension de groupes,
C.R. Acad. Sc. Paris, Serie A, tome 285, 28 novembre 1977, 929-931). A key
ingredient is the notion of fibrewise-localization.
