In binary Gaussian process classification the prior class membership probabilities are obtained by transforming a Gaussian process to the unit interval, typically either with the logistic likelihood function or the cumulative Gaussian likelihood function. Multiclass classification problems can be handled by any binary classifier by means of so-called binarization techniques, which reduces the multiclass problem into a number of binary problems. Other than introducing the mathematics behind the theory and methods behind Gaussian process classification, we compare the binarization techniques one-against-all and one-against-one in the context of Gaussian process classification, and we also compare the performance of the logistic likelihood and the cumulative Gaussian likelihood. This is done by means of two experiments: one general experiment where the methods are tested on several publicly available datasets, and one more specific experiment where the methods are compared with respect to class imbalance and class overlap on several artificially generated datasets. The results indicate that there is no significant difference in the choices of binarization technique and likelihood function for typical datasets, although the one-against-one technique showed slightly more consistent performance. However the second experiment revealed some differences in how the methods react to varying degrees of class imbalance and class overlap. Most notably the logistic likelihood was a dominant factor and the one-against-one technique performed better than one-against-all.