By a theorem of McLean, the deformation space of an associative submanifold Y of an integrable G 2 manifold ( M, ϕ ) can be identified with the kernel of a Dirac operator on the normal bundle ν of Y . Here, we generalize this to the non-integrable case, and also show that the deformation space becomes smooth after perturbing it by natural parameters, which corresponds to moving Y through ‘pseudo-associative’ submanifolds. Infinitesimally, this corresponds to twisting the Dirac operator with connections A of ν . Furthermore, the normal bundles of the associative submanifolds with Spin c structure have natural complex structures, which helps us to relate their deformations to Seiberg-Witten type equations. If we consider G 2 manifolds with 2-plane fields ( M , ϕ, λ) (they always exist) we can split the tangent space TM as a direct sum of an associative 3-plane bundle and a complex 4-plane bundle. This allows us to define (almost) λ-associative submanifolds of M , whose deformation equations, when perturbed, reduce to Seiberg-Witten equations, hence we can assign local invariants to these submanifolds. Using this we can assign an invariant to ( M , ϕ, λ). These Seiberg-Witten equations on the submanifolds are restrictions of global equations on M . We also discuss similar results for the Cayley submanifolds of a Spin(7) manifold.