Mixed order locally recurrent neural networks are proposed to build long term prediction models for nonlinear processes. In a mixed order locally recurrent network, the output of a hidden neuron is fed back to its input through several units of time delay, different hidden neurons can have different numbers of feedbacks. A sequential orthogonal training method is proposed to train locally recurrent neural networks. The first hidden neuron essentially models any underlying linear relationship in the process data with additional hidden neurons being introduced sequentially to model the relationship between the model inputs and the model residuals to improve the ability of the model to represent the underlying process. Network training is terminated when the model error on the testing data cannot be further reduced. Through this training strategy, an appropriate network topology is automatically determined. The classical Gram-Schmidt orthogonalisation technique in conjunction with regularisation is used as part of the hidden neuron selection procedure to improve the generalisation capability of the network. Applications of the technique to a continuous polymerisation process and a neutralisation process demonstrate that mixed order locally recurrent networks can provide good long-term predictions for nonlinear processes.