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The second post-Newtonian solution for the quasi-Keplerian motion of a testparticle in the gravitational field of regular Bardeen black hole is derived.The solution is formulated in terms of the test particle's orbital energy andangular momentum, as well as the mass and magnetic charge of the Bardeen blackhole. The leading effects of the magnetic charge on the test particle's orbitand motion including perihelion precession are displayed explicitly. Inparticular, it is shown that to the second post-Newtonian order the magneticcharge does not affect the test particle's orbital period.

The quasi-Keplerian motion in the regular Bardeen spacetime