  Main topic of the paper is the determination, for a compact complex manifold
$M$, of the class of manifolds $X$ which are deformation equivalent to it. If
$M$ is a complex torus, then also $X$ is so. After describing the structure of
principal holomorphic torus bundles over curves, a similar result (stability by
deformations in the large) is obtained also for the latter class of manifolds.
A section of the paper is devoted to the structure of principal holomorphic
torus bundles over tori, establishing the Riemann bilinear relations, and
exhibiting a so called Appell Humbert family, which could conjecturally give
all small deformations. Finally, a general definition is given of so called
Blanchard -Calabi manifolds, which, using an old construction of Sommese, show
that the family of complex structures on the differentiable manifold underlying
the product of a curve of genus $g\geq 2$ with a 2-dimensional complex torus
admits several distinct deformation types.
