Present paper is formulated the dual traffic assignment problem. The travel time on the edges and the primal problem Lagrange multipliers, which corresponds to the equilibrium travel time between pairs of origin and destination, were chosen as dual variables. Thus, the above problem solution is the travel time on the edges and the travel time between OD-pair on the any actually used route under the assumption of user equilibrium. The primal and dual problems of equilibrium travel time searching are considered. The volumes of the travel demand between OD-pairs were defined uniquely for the cases of linear and nonlinear network of non-intersecting routes