  Deligne's celebrated "Riemann--Hilbert correspondence" relates
representations of the fundamental group of a smooth complex algebraic variety
and regular-singular integrable connections. In this work, we show how to
arrive at a similar statement in the case of a smooth scheme $X$ over the
spectrum of a ring $R=\mathbb C[[t_1,\ldots, t_r]]/I$. On one side of the
correspondence we have representations on $R$-modules of the fundamental group
of the special fibre, and on the other we have certain integrable
$R$-connections admitting logarithmic models. The correspondence is then
applied to give explicit examples of differential Galois groups of $\mathbb
C[[t]]$--connections.
