  The origin of the ultrahigh energy cosmic ray remains being a mystery.
However, a considerable progress has been made in the past few years due to the
good quality data recorded by current cosmic ray observatories. One of the
recent achievements is obtaining firm observational evidence about the
extragalactic origin of the most energetic cosmic rays by the Pierre Auger
observatory. On the other hand, it is believed that there is a non-null
turbulent magnetic field that fills the intergalactic medium. Therefore, the
presence of the intergalactic magnetic field can play an important role on the
propagation of the ultrahigh energy cosmic rays through the Universe, which in
principle can be relevant to interpret the experimental data. In this work we
present a system of partial differential equations that describes the
propagation of the ultrahigh energy cosmic rays through the Universe, in the
presence of a turbulent intergalactic magnetic field, that includes the
diffusive and the ballistic regime of propagation and also the transition
between them. Also, as an example of application, the system of equations is
solved numerically in a simplified physical situation.
