  We generalize the vacuum static black strings with negative cosmological
constant recently discussed in literature, by including an electromagnetic
field. These higher-dimensional configurations have no dependence on the
`compact' extra dimension, and their boundary topology is the product of time
and $S^{d-3}\times S^1$ or $H^{d-3}\times S^1$. Rotating generalizations of the
even dimensional black string configurations are considered as well. Different
from the static, neutral case, no regular limit is found for a vanishing event
horizon radius. We explore numerically the general properties of such solutions
and, using a counterterm prescription, we compute their conserved charges and
discuss their thermodynamics. We find that the thermodynamics of the black
strings follows the pattern of the corresponding black hole solutions in AdS
backgrounds.
