The discovery is reported of a variable X-ray source at midgalactic latitude in the globular cluster NGC 1851, and observations are reported which confirm the existence of variable X-ray sources in NGC 7078 and NGC 6441. The new source, designated MX 0513-40, was found to vary in intensity by a factor of at least 5 over a sixteen-day period and to have a hard spectrum as compared to that of the Crab Nebula in the energy range from 1 to 10 keV. The source in NGC 7078 (3U 2131+11) was found to vary by more than a factor of 2 over a 500-day period. Strong evidence of variability is presented for the source in NGC 6441 (3U 1746-37). It is concluded that both MX 0513-40 and 3U 2131+11 are probably stellar objects and are no more than about 160 kpc distant.