Several machine learning problems arising in natural language processing can be modeled as a sequence labeling problem. Gaussian processes (GPs) provide a Bayesian approach to learning such problems in a kernel based framework. We develop Gaussian process models based on pseudo-likelihood to solve sequence labeling problems. The pseudo-likelihood model enables one to capture multiple dependencies among the output components of the sequence without becoming computationally intractable. We use an efficient variational Gaussian approximation method to perform inference in the proposed model. We also provide an iterative algorithm which can effectively make use of the information from the neighboring labels to perform prediction. The ability to capture multiple dependencies makes the proposed approach useful for a wide range of sequence labeling problems. Numerical experiments on some sequence labeling problems in natural language processing demonstrate the usefulness of the proposed approach. © Springer International Publishing AG 2016.