In this paper, we investigate online nonlinear regression and introduce novel algorithms based on the long short term memory (LSTM) networks. We first put the underlying architecture in a nonlinear state space form and introduce highly efficient particle filtering (PF) based updates, as well as, extended Kalman filter (EKF) based updates. Our PF based training method guarantees convergence to the optimal parameter estimation under certain assumptions. We achieve this performance with a computational complexity in the order of the first order gradient based methods by controlling the number of particles. The experimental results illustrate significant performance improvements achieved by the introduced algorithms with respect to the conventional methods.