This paper presents and analyzes a point-tomultipoint (P2MP) network that uses a number of freespace optical (FSO) links for data transmission from the central node to the different remote nodes of the network. A common backup radio frequency (RF) link can be used by the central node for data transmission to any remote node in case any one of the FSO links fails. Each remote node is assigned a transmit buffer at the central node. Considering the transmission link from the central node to a tagged remote node, we study various performance metrics. Specifically,we study the throughput from the central node to the tagged node, the average transmit buffer size, the symbol queuing delay in the transmit buffer, the efficiency of the queuing system, the symbol loss probability, and the RF link utilization. Numerical examples are presented to compare the performance of the proposed P2MP hybrid FSO/RF network with that of a P2MP FSO-only network and show that the P2MP hybrid FSO/RF network achieves considerable performance improvement over the P2MP FSO-only network.