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We study the infinitesimal deformations of a proper nearly parallelG_2-structure and prove that they are characterized by a certain first orderdifferential equation. In particular we show that the space of infinitesimaldeformations modulo the group of diffeomorphisms is isomorphic to a subspace ofco-closed $\Lambda^3_{27}$-eigenforms of the Laplace operator for theeigenvalue 8 scal/21. We give a similar description for the space ofinfinitesimal Einstein deformations of a fixed nearly parallel G_2-structure.Moreover we show that there are no deformations on the squashed S^7 and onSO(5)/SO(3), but that there are infinitesimal deformations on the Aloff-Wallachmanifold N(1,1) = SU(3)/U(1).

Deformations of nearly parallel G_2-structures