Local thermodynamic models are used to accelerate dynamic optimization calculations. The optimization problem is solved with the sequential approach. The main calculation effort in this optimization is the evaluation of the sensitivities of the objective function and constraints w.r.t. the parameters. A new approach is tried out for using local thermodynamic models in the sensitivity estimation. The local model must be updated to ensure sufficient accuracy. The local model updates generate discontinuities which give trouble for the integrator. To avoid these problems the special purpose integrator DASSLM was developed. DASSLM simultaneously integrates one rigorous trajectory and the N-parameter+1 local model trajectories needed for calculating the sensitivities by a forward difference formula. The simultaneous calculation of the local model and the rigorous model trajectories give at all times the error in the local model. This error can be used to update the local model according to a predefined tolerance. The steplength in DASSLM is determined only with information from the rigorous trajectory, the updates does thus not affect the steplength. The results show that the DASSLM local model approach is computationally efficient and stable, but that the accuracy of the gradients are reduced. In addition to the DASSLM integrator, the DASAC integrator is tried out with local thermodynamic models.