In the design and analysis of air traffic control systems the considerations which lead to the adoption of a particular route and control structure in a given airspace are partially governed by the traffic demands between given points within the area concerned. When air traffic control plans are being developed for use in a particular area, it is of prime importance to know where the main A.T.C. problems lie and to concentrate planning effort in these parts of the system. The development of routing and control procedures should take into account the degree of risk associated with any particular route structure. In the case of near mid-air collisions (NMAC's) or collisions, quantitative prediction of the risk involved is difficult. In this paper a simple theoretical method for predicting the number of NMAC's for a particular route structure is given. Such a method has been used practically for determining the amount of control required for a particular off-airways area and to help determine the optimum control procedures for air traffic planning in that area.