We propose a novel multicast communications model, called RingNet, which is a combination of logical trees and logical rings for multicast communications. Based on RingNet, we propose a reliable totally-ordered group multicast protocol for mobile Internet. The network entities in the top logical ring of the RingNet hierarchy are responsible for totally-ordering messages. All the network entities in all the logical rings are responsible for reliably transmitting multicast messages to their next nodes, children nodes, or their attaching mobile hosts, even in handoffs. The proposed protocol runs in a parallel and distributed way in the sense that each network entity only maintains information about its possible neighbors, and independently decides whether, when, and where to order, forward, and deliver multicast messages. We prove that, compared with the multicast protocol without ordering requirement, our totally-ordered multicast protocol provides the same multicast throughput, only with limited overhead on message latency and buffer sizes.