The paper combines methods from Bayesian statistics with ideas from fuzzy set theory to generalize Bayesian methods both for samples of fuzzy data and for prior distributions with non-precise parameters. Applying the principle of propagation of fuzziness we introduce a fuzzy valued likelihood function, Bayes' theorem for both fuzzy data and fuzzy priors, a fuzzy Bayes' estimator, fuzzy predictive densities and distributions, and fuzzy H.P.D.-regions.