  We describe the family of real structures $\sigma$ on principal holomorphic
torus bundles $X$ over tori, and prove its connectedness when the complex
dimension is at most three. From this and previous results of the authors
follows that the differentiable type (more precisely, the orbifold fundamental
group) determines the deformation type of the pair $(X, \sigma)$ provided we
have complex dimension at most three, fibre dimension one, and a certain
'reality' condition on the fundamental group is satisfied.
