The galliumchloride detector operated by the GALLEX-collaboration in the Gran Sasso Underground Laboratory responds primarily to pp-neutrinos. They are produced in the primary fusion reaction of hydrogen into deuterium and directly coupled to the solar luminosity. Standard Solar Models predict ca. 58% of the total signal expected in GALLEX (123-132 SNU) to be due to pp-neutrinos. The relative pp-neutrino dominance becomes even larger if the deficit of higher energy neutrinos (as observed in the Homestake- and Kamiokande experiments) is considered. During the first data taking period, 15 solar runs had been performed within the exposure period 14.5.1991 - 29.4.1992. The result, 81 {+-} 17 {+-} 9 SNU provided the first experimental evidence for pp-neutrinos from the Sun. At the same time, it confirmed the depression of higher energy neutrino fluxes relative to the model predictions. Here the authors report the results of 15 more solar neutrino runs, covering the period 19.8.92 - 13.10.93. They obtain 78 {+-} 13 {+-} 5 SNU. Evaluated together, the result for all 30 runs is 79 {+-} 10 {+-} 6 SNU. While the SNU rate of GALLEX I is well reproduced the statistical error has been reduced so substantially that a value of signal +2{sigma}more » is required to accommodate not only pp-and pep- but also the {sup 7}Be-neutrino induced {sup 71}Ge-production. Contrary, the fate of {sup 8}B-neutrinos has only little discernible effect on the GALLEX data. In conclusion, with the present errors GALLEX constitutes a 2.5 {sigma} problem for {sup 7}Be neutrinos within the frame of {open_quotes}astrophysical{close_quotes} solutions. Alternatively, the particle physics solution (MSW-effect) can consistently explain all available solar neutrino results, leading to a most probable mass scale with the muon-neutrino at approximately 3 meV (milli-eV). However, since the GALLEX result allows the presence of pp and pep neutrinos at full strength. the latter explanation of the data is not forced.« less