The paper studies the existence of periodic solutions of a perturbed relativistic Kepler problem of the type \(\begin{aligned} \dfrac{\textrm{d}}{\textrm{d}t}\left( \frac{m\dot{x}}{\sqrt{1-|\dot{x}|^{2}/c^{2}}}\right) = -\alpha \frac{x}{|x|^{3}} + \varepsilon \, \nabla _{x} U(t,x), \qquad x \in \mathbb {R}^d\setminus \{0\}, \end{aligned}\) with \(d=2\) or \(d=3\) , bifurcating, for \(\varepsilon \) small enough, from the set of circular solutions of the unperturbed system. Both the case of the fixed-period problem (assuming that U is T-periodic in time) and the case of the fixed-energy problem (assuming that U is independent of time) are considered.
