  In this paper, we derive rotating black string solutions in the presence of
two kinds of nonlinear electromagnetic fields, so called Born-Infeld and power
Maxwell invariant. Investigation of the solutions show that for the Born-Infeld
black string the singularity is timelike and the asymptotic behavior of the
solutions are anti-deSitter, but for power Maxwell invariant solutions, depend
on the values of nonlinearity parameter, the singularity may be timelike as
well as spacelike and the solutions are not asymptotically anti-deSitter for
all values of the nonlinearity parameter. Next, we calculate the conserved
quantities of the solutions by using the counterterm method, and find that
these quantities do not depend on the nonlinearity parameter. We also compute
the entropy, temperature, the angular velocity, the electric charge and the
electric potential of the solutions, in which the conserved and thermodynamics
quantities satisfy the first law of thermodynamics.
