Most of the variable phenomena of high-luminosity (il0 3G erg s~:) stellar X-ray sources can be explained, at least qualitatively, within the general framework of binary accretion models in which thermal X-rays are emitted in the vicinity of a neutron star or blackhole by plasma that has flowed downhill from the surface of a nuclear burning companion and been heated by conversion of its gravitational potential energy. The yield of X-ray energy in this process is so high, exceeding in some cases 0.1c per unit mass, that X-ray luminosities in excess of 10 L 0 can be generated with accretion rates of only ~10~ M @ per year. Since the transfer process depends strongly on many parameters that specify the relevant properties of two stars and their interaction, one finds a remarkable variety and range of X-ray phenomena. If the compact object is a magnetized neutron star, rotation will cause its X-ray emission ; pattern to sweep over a distant observer and thereby produce regular pulsations like those observed with periods in the range from 1 to 10 seconds. Orbital motions can cause regular eclipses and absorption dips like those observed with periods in the range from hours to days. Changes in the rate of mass loss by the nuclear burning star or in the transfer efficiency can account for the variations in intrinsic X-ray luminosities that appear as flares, novae and on-off transitions. Irregularities in the flow of plasma near the compact star can also affect the intrinsic luminosity and appear as erratic fluctuations, spikes and shot-noise in the observed intensity.Recently Babushkina et al. (1975) discovered a new and qualitatively distinct kind of X-ray variation that may also fit within the general binary accretion model, though it was entirely unpredicted and is, indeed, a most surprising phenomenon. In data obtained by the Kosmos 428 satellite in 1971 they found two brief, intense "bursts" of X-rays recorded by detectors sensitive above 40 keV from two different sources lying within about 20 degrees of the galactic center. In both bursts the intensities rose to peak values in about Is and decayed in <10s, and the total energy fluxes at the detector were of the order of 3xl0 -6 ergs cm -2 . The bursts differed from typical gamma ray bursts in having much softer spectra and much smaller energy fluxes.