A hybrid neural network-first principles modeling scheme is developed and used to model a fedbatch bioreactor. The hybrid model combines a partial first principles model, which incorporates the available prior knowledge about the process being modeled, with a neural network which serves as an estimator of unmeasured process parameters that are difficult to model from first principles. This hybrid model has better properties than standard “black-box” neural network models in that it is able to interpolate and extrapolate much more accurately, is easier to analyze and interpret, and requires significantly fewer training examples. Two alternative state and parameter estimation strategies, extended Kalman filtering and NLP optimization, are also considered. When no a priori known model of the unobserved process parameters is available, the hybrid network model gives better estimates of the parameters, when compared to these methods. By providing a model of these unmeasured parameters, the hybrid network can also make predictions and hence can be used for process optimization. These results apply both when full and partial state measurements are available, but in the latter case a state reconstruction method must be used for the first principles component of the hybrid model.