  We discuss the motion of electrically and magnetically charged particles in
the electromagnetic swirling universe. We show that the equations of motion can
be decoupled in the Hamilton-Jacobi formalism, revealing the existence of a
fourth constant of motion. The equations of motion can be analytically
integrated. The solutions are presented in terms of elementary and elliptic
functions. In addition, we discuss the possible orbits for both uncharged
particles (in which case the motion is geodesic) and charged particles,
respectively. A typical orbit is bounded in the radial direction and escapes to
infinity in the $z-$ direction. However, the presence of the electromagnetic
fields also leads to the existence of planar orbits.
