A silicate optical fiber comprises a graded index silicate core co-doped with aluminum oxide, phosphorus oxide, germanium oxide and fluorine in unique compositions that we have discovered allow multimode, multi-wavelength operation without significant intermodal dispersion. Illustratively, the core comprises a multiplicity of compositions whose refractive indices are graded from a maximum at or near the center of the core to a minimum at the interface with the cladding. Each core composition resides within a sub-volume of a 5 dimensional phase space in which an optimum core profile shape is essentially constant over the wavelength range of operation of the fiber. For operation in the wavelength range of about 0.78 .mu.m to 1.55 .mu.m, each composition preferably comprises no more than approximately 6 mole % Al.sub.2O.sub.3, 9 mole % P.sub.2O.sub.5, 6 mole % GeO.sub.2, 6 mole % F, and 90-100 mole % SiO.sub.2.