FANET (Flying Ad Hoc Network), similar to mobile peer-to-peer networks MANET and vehicular peer-to-peer networks VANET, represents a special type of peer-to-peer ad hoc network based on UAVs. Such a network has the ability to selforganize and adapt and is characterized by a dynamic changing topology. Special routing algorithms developed due to their specific features are need to organize FANET. The article gives a short overview of the existing FANET algorithms, as well as of the algorithms based on the swarm intelligence algorithms such as ant colony optimization. The experimental analysis was conducted, that proved the possibility of efficient application of ant colony optimization algorithm. The analysis was performed with the AntHocNet protocol simulating the behavior of ants in wildlife to solve the routing problems in FANETs.