  In the present paper we prove a uniqueness theorem for stationary multi black
hole configurations with Kaluza-Klein asymptotic in a certain sector of 5D
Einstein-Maxwell gravity. We show that such multi black hole configurations are
uniquely specified by the interval structure, angular momenta of the horizons,
magnetic charges and the magnetic flux. A straightforward generalization of the
uniqueness theorem for 5D Einstein-Maxwell-dilaton gravity is also given.
