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In this paper, we present a theory on the stationary motion of a one-axlerailway vehicle along a circular curve in the presence of single- or double-pointcontact. The rail and the wheel profiles may be either stylized or real andas an example we take the profile combination UIC60 1:40 S1002. The mathematical model of the system is based on De Pater's first-ordertheory [1]. The geometrical contact problem between wheel and rail is solvedby using a modified Newton-Raphson procedure. Both the cases with and withoutfriction are considered. When friction is present, the non-linear Kalker creeplaw [6, 7] is used to describe the physical contact. For various values of the friction coefficient, the cant angle and thecurvature of the track, the contact forces are presented as functions of thevelocity parameter C [sub v] = V [sup 2] / V [sub eq] [sup 2] , where V is the velocity of the vehicleand V [sub eq] is the equilibrium velocity of the frictionlesscase. For the case of stylized profiles in which both the wheel treads and thewheel flanges are conical, and the rail cross sections are circular, we havedetermined the velocity range with single point contact in dependence on thefriction coefficient, the conicity of the tread, the curvature of the trackand the cant angle. [ABSTRACT FROM AUTHOR]