ZMA is a proprietary blend of Zinc bound to monomethionine, Magnesium bound to aspartate, and the vitamin B6 (Pyridoxine). It is sometimes reported to give users 'weird, vivid dreams'.
This claim has not been investigated much, but a pilot study[1] suggests that a dose of 250mg pyridoxine can alter dream perception in college aged men, through a hypothesized increased conversion of tryptophan to serotonin. This dose of B6, however, is much higher than that occurring in ZMA products; which tends to range in the 10-50mg range and usually at the lower end.
One other study has reported synergism between B6 and Magnesium in regards to anxiety reduction, when the subjects were women experiencing PMS;[2] it is theoretically possible that the ZMA formulation enhances the actions of pyridoxine allowing the previous research's results to be relevant.