Context-dependent deep neural network HMMs have been shown to achieve recognition accuracy superior to Gaussian mixture models in a number of recent works. Typically, neural networks are optimized with stochastic gradient descent. On large datasets, stochastic gradient descent improves quickly during the beginning of the optimization. But since it does not make use of second order information, its asymptotic convergence behavior is slow. In regions with pathological curvature, stochastic gradient descent may almost stagnate and thereby falsely indicate convergence. Another drawback of stochastic gradient descent is that it can only be parallelized within minibatches. The Hessian-free algorithm is a second order batch optimization algorithm that does not suffer from these problems. In a recent work, Hessian-free optimization has been applied to a training of deep neural networks according to a sequence criterion. In that work, improvements in accuracy and training time have been reported. In this paper, we analyze the properties of the Hessian-free optimization algorithm and investigate whether it is suited for cross-entropy training of deep neural networks as well.