  The aim of this paper is to study the pro-algebraic fundamental group of a
compact Kaehler manifold. Following work by Simpson, the structure of this
group's pro-reductive quotient is already well understood. We show that
Hodge-theoretic methods can also be used to establish that the pro-unipotent
radical is quadratically presented. This generalises both Deligne et al.'s
result on the de Rham fundamental group, and Goldman and Millson's result on
deforming representations of Kaehler groups, and can be regarded as a
consequence of formality of the schematic homotopy type. New examples are given
of groups which cannot arise as Kaehler groups.
