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Agreement problems and their solutions are essential to fault-tolerant distributed computing. Over the years, different assumptions on failures have been considered, but most of these assumptions were focusing on either processes or links. In contrast, we examine a model where both links and processes can fail. In this model we devise a unified lower bound for resilience to both classes of faults. We show that the bound is tight by devising a simple retransmission scheme that allows optimally resilient algorithms to be constructed from well known algorithms by transparently adding link-fault tolerance. Our results show that when considering multiple independent failure modes, resilience bounds are not necessarily additive. (C) 2014 Elsevier Inc. All rights reserved.