Local area ring networks operate without causing collision, and without station competition. It is quite opposite to currently the most popular technology, Ethernet network, where collisions may occur in a large amount. These two features of the ring networks provide significantly better performance and greater amount of data that can be effectively transmitted in the same time unit. This is especially true during high network load. This paper deals with the comparison of the efficiency of the two ring networks: Token Ring and FDDI (Fiber Distributed Data Interface), taking into account the access mechanisms to network stations. In relation to this issue general information about the efficiency of the Ethernet is also described.