The one- versus two-degree-of-freedom vortex-induced vibrations of a circular cylinder are investigated on the basis of direct numerical simulation results. The Reynolds number, based on the oncoming flow velocity and cylinder diameter, is set to 3900. Three cases are examined: the elastically mounted body is free to oscillate either in the direction aligned with the current (in-line direction; IL case), in the direction normal to the current (cross-flow direction; CF case), or in both directions (IL+CF case). In each case, the behavior of the flow–structure system is studied over a range of values of the reduced velocity (inverse of the oscillator natural frequency). The in-line and cross-flow responses observed in the IL+CF case substantially differ from their one-degree-of-freedom counterparts, especially in the intermediate reduced velocity region. In this region, no vibrations develop in the IL case and in-line oscillations only occur if cross-flow motion is allowed. These in-line oscillations are accompanied by a major increase of the cross-flow responses, compared to the CF case. The two-degree-of-freedom vibrations are associated with the emergence of large-amplitude higher harmonics in the fluid force spectra. These aspects and more specifically the impact of the existence of a degree-of-freedom and oscillations in a given direction, on the fluid force and structural response in the perpendicular direction, do not seem to be systematically connected to changes in wake topology. Here, they are discussed in light of the orientation and magnitude of the instantaneous flow velocity seen by the moving body.