This paper provides a preview of the former stages through which the market of express postal services had gone and the possibilities of further development, both on the global and local level. The aim of this paper is to complete an estimation of the need for this type of express services using the competitive Lotka–Volterra model in Serbia. In order to reduce the complexity of the process, the division of competition was conducted in two segments: the public operator and the private segment (comprised of all private operators). The given model provides a description of a dynamic competition relationship by indicating the existence of the equilibrium point between the public and the private sectors, and the conditions of its stability. The obtained values indicate that the private sector affects the public operator. The existing predator-prey relationship gives preference to the private sector and can be described by the Lotka-Volterra model.