This thesis introduces a new multitask learning model for Bayesian neural networks based on ideas borrowed from statistics: random regression coefficient models. The output of the model is a combination of a common hidden layer and a task specific hidden layer, one for each task. If the tasks are related, the goal is to capture as much structure as possible in the common layer, while the task specific layers reflect the fine differences between the tasks. This can be achieved by giving different priors for different model parameters.The experiments show that the model is capable of exploiting the relatedness of the tasks to improve its generalisation accuracy. As for other multitask learning models, it is particularly effective when the training data is scarce. The feasibility of applying the introduced multitask learning model to Brain Computer Interface problems is also investigated.