In this work we argue for relevant logics as a basis for paraconsistent epistemic logics. In order to do so, a paraconsistent nonmonotonic multi-agent epistemic logic,MDR(for Modal Defeasible Relevant), is briefly introduced. InMDReach agent has two kinds of belief: an absolute belief that P, represented by AiP, and a defeasible belief that P, represented by DiP. Therefore, an agent can reason with his own absolute and defeasible beliefs about the world and also reason about his beliefs about other agents' beliefs both absolute and defeasible. A theorem is presented showing some patterns of reasoning inMDR. Avron's relevant logicRMI→ s compared proof theoretically with Anderson and Belnap's relevant logicsRandRMand also with Da Costa's paraconsistent logic CI, with respect to some desired properties of absolute and defeasible beliefs. Then we can understand whyRMIwas chosen to be the underlying logic for the monotonie part (the absolute beliefs) ofMDR, and had to be modified and integrated with a nonmonotonic logic in order to be the underlying logic for the nonmonotonic part (defeasible beliefs).