Summary: In many distributed-memory parallel computers and high-speed communication networks, the exact structure of the underlying communication network may be ignored. These systems assume that the network creates a complete communication graph between the processors, in which passing messages is associated with communication latencies. In this paper we explore the impact of communication latencies on the design of broadcasting algorithms for fully connected message-passing systems. For this purpose, we introduce the postal model that incorporates a communication latency parameter \(\lambda\geq 1\). This parameter measures the inverse of the ratio between the time it takes an originator of a message to send the message and the time that passes until the recipient of the message receives it. We present an optimal algorithm for broadcasting one message in systems with \(n\) processors and communication latency \(\lambda\), the running time of which is \(\Theta((\lambda\log n)/\log(\lambda+ 1))\). For broadcasting \(m\geq 1\) messages, we first examine several generalizations of the algorithm for broadcasting one message and then analyze a family of broadcasting algorithms based on degree-\(d\) trees. All the algorithms described in this paper are practical event-driven algorithms that preserve the order of messages.