Given an immersion of an N-dimensional manifold into \((N+K)\)-dimensional general affine space, three affine invariant tensors are constructed on the manifold that depend, respectively, on the second, third, and fourth order information of the immersion. For \(K=2\), \(N>2\) it is proven that the first two tensors are sufficient to discern between two different affine immersions. For \(N=2=K\) and \(K=1\) it is proven that all three of the tensors are sufficient to discern between two affine immersions.