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Distributed computing systems require methods for a participant's decision about its trust in other entities. A similar problem exists in the area of Public Key Infrastructures (PKIs) where the verifier's trust in the issuer of a public key certificate is a well-known prerequisite for the acceptance of the certificate. This work presents a method for the assignment, the storage, the propagation and the verification of trust in a distributed system which is based on a PKI trust management approach. A participant's trust causes the issuing of a digital certificate binding a privilege for the proper fulfillment of a certain task to the trusted entity. These certificates are stored in a distributed manner in the system and, therefore, are available to any other participant for its trust decisions. We describe the processes for the certification and the verification of these trust privileges. Additionally, a formal model of the trust verification process is presented. An example illustrates the application of the method and the model.