- User-equilibrium (UE) assignment is widely used in predictions of travel on roadway systems. It is well known that total link flows are uniquely determined by the UE assumption (under certain technical conditions); however, route flows are not. Route flows have become increasingly important in practical applications as the variety of analyses performed on traffic assignment results expands. The purpose of this paper is to examine to what extent results of analyses may be influenced from this issue of non-uniqueness. As a case study, we use a medium size network for the roadway system in Israel. We obtain a precise UE solution, determine the set of UE mutes in this solution, and generate many alternative route-flow UE solutions. The effects of differences among solutions are analysed at the route level and for two types of applications: analyses of 'link of interest' and analyses related to licence plate surveys. The results show that for almost every OD pair with multiple UE routes the route flows are nearly completely arbitrary. Substantial arbitrariness remains in aggregate analyses as well; for example, for 9% of the links the origin cannot be determined for at least half of the flow. OD shares within a link are the basis for other advanced modeling methods, such as OD matrix estimation, further emphasising the importance of the issue. To solve this disturbing problem, an additional behavioral assumption is needed. The only assumption suggested to date, in various forms, is that proportions of flow on alternative route segments are the same for all travellers, regardless of their origin or destination. We examine this assumption, argue that it is reasonable, and recommend it for practical applications.