Using the data by Geyer et al. (1983) and by White and Shawl (1987) it has been looked for the dependence of the ellipticity of Galactic globular clusters on luminosity. There is evidence that the moderate bright objects are the roundest, while the most luminous as well as the weaker globulars are more flat,tened, on the average. Since the paper by Pease and Shapley (1917) we know that most of the globular clusters are somewhat flattened. Generally it has been accepted that the main cause of the ellipticity of the globular clusters is rotation, even if other processes as interactions with the Galaxy's tidal field or effects of an anisotropic velocity dispersion tensor have been discussed, too. Also part of the flattening of the globulars may be relics of the initial conditions, and it appears tha.t the study of the shapes of the clusters can tell something about cluster formation.Beginning with Shapley and Sawyer (1927b) and Shapley (1930) a number of determinations of axial ratios of globulars of the Milky Way System, the Magellanic Clouds, and M31 using different techniques have been published (Kholopov 1952, 1953, Lindsay 1956, Dickens and Woolley 1967, Kadla et al. 1976, 1977, Frenk and Fall 1982, Geyer et al. 1983, Spasova and Staneva 1984, Staneva et al. 1985, White and Shawl 1987, Lupton 1989, Davoust and Prugniel 1990, D'Onofrio et al. 1994). There are many attempts to correlate the ellipticity with other properties of the globular clusters, e.g. with position in the parent galaxy, metallicity, luminosity, and, in connection with open clusters, with age. Most of these investigations are with uncertain or even adverse results.A striking phenomenon concerns the most luminous globular clusters in different galaxies: w Centauri in the Milky Way System, Mayall I1 in M31, and NGC 1835 in the Large Magellanic Cloud are not only the brightest but also the most flattened globulars in their parent galaxies (van den Bergh 1983, 1996, Pritchet and van den Bergh 1984. In addition, according to Hesser et al. (1984) four of the six brightest known globular clusters in the giant elliptical galaxy NGC 5128 are noticeably flattened. Since the total of these observational facts is hardly fortuitous the question arises if there exists a general relation between the ellipticity and the ,luminosity of globular clusters. After van den Bergh and Morbey (1984) the clusters in the Large Magellanic Cloud showing large ellipticity are brighter than those of low flattening. But it is worth mentioning that this sample is contaminated by open clusters. In contrast to this result Davoust and Prugniel (1990) from a compilation of axial ratios of globular clusters of the Galaxy and M31 have shown that with the mentioned exceptions of w Centauri and Mayall I1 the brightest globular clusters are also the roundest. Both the papers by Lupton (1990) and by D'Onofrio et al. (1994) on globular clusters in M3 1 , however, do not contain conclusive results on a ellipticity-luminosity dependence.The aim of the present paper is to look for a corr...