  We study the infinitesimal deformations of a proper nearly parallel
G_2-structure and prove that they are characterized by a certain first order
differential equation. In particular we show that the space of infinitesimal
deformations modulo the group of diffeomorphisms is isomorphic to a subspace of
co-closed $\Lambda^3_{27}$-eigenforms of the Laplace operator for the
eigenvalue 8 scal/21. We give a similar description for the space of
infinitesimal Einstein deformations of a fixed nearly parallel G_2-structure.
Moreover we show that there are no deformations on the squashed S^7 and on
SO(5)/SO(3), but that there are infinitesimal deformations on the Aloff-Wallach
manifold N(1,1) = SU(3)/U(1).
