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A class of spinning magnetic string in 4-dimensional Einstein-dilaton gravitywith Liouville type potential which produces a longitudinal nonlinearelectromagnetic field is presented. These solutions have no curvaturesingularity and no horizon, but have a conic geometry. In these spacetimes,when the rotation parameter does not vanish, there exists an electric field,and therefore the spinning string has a net electric charge which isproportional to the rotation parameter. Although the asymptotic behavior ofthese solutions are neither flat nor (A)dS, we calculate the conservedquantities of these solutions by using the counterterm method. We alsogeneralize these four-dimensional solutions to the case of $(n+1)$-dimensionalrotating solutions with $k\leq[n/2]$ rotation parameters, and calculate theconserved quantities and electric charge of them.

Magnetic Strings in Einstein-Born-Infeld-Dilaton Gravity