We propose a new hybrid fault model for clock synchronization and single-round (approximate) agreement in synchronous distributed systems (This research has been conducted in our SynUTC-project, see http://www.auto.tuwien.ac.at/Projects/SynUTC/, supported by the Austrian START programme Y41-MAT. Part of it has been presented at DSN'01.) which accurately captures both node and link faults. Unlike conventional ``global'' fault models, which rest upon the total number of faulty nodes in the system, it solely relies upon the number of faults in any two non-faulty nodes' ``perceptions'' ---conveyed by the messages from all other nodes--- of the system. This way, arbitrary node and communication faults, including receiver-caused omission and time/value faults, can be modeled properly. We show that both the consistent broadcast primitive of Srikanth & Toueg and our Fault-Tolerant Interval convergence function (emulating Lundelius & Lynch's Fault-Tolerant Midpoint algorithm as well) can be analyzed under this model. As far as link faults are concerned, our analysis reveals that both algorithms require 4\ia+2\is+2\io+1 nodes for tolerating at most \ia, \is, and \io asymmetric, symmetric, and omission faults at each receiving node. Keywords: Fault-tolerant distributed systems, fault models, link failures, consistent broadcasting, convergence functions, interval-based clock synchronization.