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We show that germanium-doped graded-index multimode silica fibers can exhibit relatively high conversion efficiencies (∼6.5%) for second-harmonic generation when excited at 1064 nm. This frequency-doubling behavior is also found to be accompanied by an effective downconversion. As opposed to previous experiments carried out in single- and few-mode fibers where hours of preparation were required, in our system, these χ^(2) related processes occur almost instantaneously. The efficiencies observed in our experiments are, to the best of our knowledge, among the highest ever reported in unprepared fibers.