In this paper, we study circular geodesic motion of test particles and photons in the Bardeen and Ayon-Beato-Garcia (ABG) geometry describing spherically symmetric regular black-hole or no-horizon spacetimes. While the Bardeen geometry is not exact solution of Einstein's equations, the ABG spacetime is related to self-gravitating charged sources governed by Einstein's gravity and nonlinear electrodynamics. They both are characterized by the mass parameter m and the charge parameter g. We demonstrate that in similarity to the Reissner-Nordstrom (RN) naked singularity spacetimes an anti-gravity static sphere should exist in all the no-horizon Bardeen and ABG solutions that can be surrounded by a Keplerian accretion disc. However, contrary to the RN nakedsingularity spacetimes, the ABG no-horizon spacetimes with parameter g/m > 2 can contain also an additional inner Keplerian disc hidden under the static anti-gravity sphere. Properties of the geodesic structure are reflected by simple ob