We experimentally demonstrate the realization of a tunable true-time delay for microwave signals by exploiting cross gain modulation among counter-propagating optical beams in a semiconductor optical amplifier. Broadband operation from ∼5 to ∼35 GHz is observed. The physical effect originates from the combination of carrier dynamics and propagation effects, and the experimental results are well accounted for by a numerical model. We find that, in contrast to the case of the co-propagating beams, the bandwidth is not limited by the lifetime of excited carriers. The trade-off between the magnitude of the true-time delay and the microwave bandwidth is discussed. © 2011 American Institute of Physics.