  Effects of a uniform (electro-) magnetic background field are investigated in
the two-flavor nonlocal Polyakov-loop extended Nambu--Jona-Lasinio (PNJL)
model. Temperature-dependences of the chiral order-parameter and the
Polyakov-loop are investigated under the magnetic field. In the nonlocal PNJL
model with four-dimensional momentum dependent distribution function,
pseudo-critical temperatures of the chiral and deconfinement transitions are
coincident each other even if the magnetic field is strong. It means that we
can check the reliability of the distribution function under the strong
magnetic field by comparing with lattice QCD data, particularly from the
viewpoint of the entanglement between the chiral and deconfinement transitions.
