  Nearly K\"ahler manifolds are the Riemannian 6-manifolds admitting real
Killing spinors. Equivalently, the Riemannian cone over a nearly K\"ahler
manifold has holonomy contained in G2. In this paper we study the deformation
theory of nearly K\"ahler manifolds, showing that it is obstructed in general.
More precisely, we show that the infinitesimal deformations of the homogeneous
nearly K\"ahler structure on the flag manifold are all obstructed to second
order.
