This paper introduces a new approach to forecast pooling methods based on a nonparametric prior for the weight vector combining predictive densities. The first approach places a Dirichlet process prior on the weight vector and generalizes the static linear pool. The second approach uses a hierarchical Dirichlet process prior to allow the weight vector to follow an infinite hidden Markov chain. This generalizes dynamic prediction pools to the nonparametric setting. We discuss efficient posterior simulation based on MCMC methods. Detailed applications to short-term interest rates, realized covariance matrices and asset pricing models show the nonparametric pool forecasts well.