An apparatus for ascertaining out-of-roundnesses of a wheel of a railbound vehicle when passing over a rail designed as a measuring section (1, 1') in the direction of travel x at the travel velocity v, comprising - a first measuring subsection (1.1, 1.1'), which extends over a length L1, and includes a first measuring device having force transducers for detecting the contact force F of the wheel over the length L1, and comprising a second measuring subsection (1.2, 1.2'), which extends over a length L2 and includes a second measuring device for ascertaining the actual circumference U ist of the wheel, - the length L1 of the first measuring subsection (1.1, 1.1') corresponding at least to the nominal circumference U nom of the wheel; and comprising - an electronic evaluation unit for receiving and processing the measured values detected with the aid of the first measuring device and the second measuring device; - the length L2 of the second measuring subsection (1.2, 1.2') being greater than the length L1 of the first measuring subsection (1.1, 1.1'); and - the second measuring device being formed from - - acceleration transducers for detecting the acceleration a applied by the wheel to the rail over the length L2 of the second measuring subsection (1.2, 1.2'); and - the evaluation unit being designed to generate a continuous force signal form F(t) from the measured values of the first measuring device over the length L1; and to generate - a further signal form from the measured values of the second measuring device over the length L2, from which, based on the travel velocity v, the actual circumference U ist of the wheel or the time period Δt corresponding to the rolling of the actual wheel circumference U ist on the second measuring subsection (1.2, 1.2') may be derived; - the ascertainment of the out-of-roundnesses of the wheel being based on a segment of the force signal form F(t), which corresponds to the actual circumference U ist or the time period Δt. - a first measuring subsection (1.1, 1.1'), which extends over a length L1, and includes a first measuring device having force transducers for detecting the contact force F of the wheel over the length L1, and comprising a second measuring subsection (1.2, 1.2'), which extends over a length L2 and includes a second measuring device for ascertaining the actual circumference U ist of the wheel, - the length L1 of the first measuring subsection (1.1, 1.1') corresponding at least to the nominal circumference U nom of the wheel; and comprising - an electronic evaluation unit for receiving and processing the measured values detected with the aid of the first measuring device and the second measuring device; - the length L2 of the second measuring subsection (1.2, 1.2') being greater than the length L1 of the first measuring subsection (1.1, 1.1'); and - the second measuring device being formed from - - acceleration transducers for detecting the acceleration a applied by the wheel to the rail over the length L2 of the second measuring subsection (1.2, 1.2'); and - - acceleration transducers for detecting the acceleration a applied by the wheel to the rail over the length L2 of the second measuring subsection (1.2, 1.2'); and - the evaluation unit being designed to generate a continuous force signal form F(t) from the measured values of the first measuring device over the length L1; and to generate - a further signal form from the measured values of the second measuring device over the length L2, from which, based on the travel velocity v, the actual circumference U ist of the wheel or the time period Δt corresponding to the rolling of the actual wheel circumference U ist on the second measuring subsection (1.2, 1.2') may be derived; - the ascertainment of the out-of-roundnesses of the wheel being based on a segment of the force signal form F(t), which corresponds to the actual circumference U ist or the time period Δt.