Raman amplification in silica and fluoride glass fibers is studied experimentally and theoretically. Two tunable dye lasers are employed to provide pump and signal light. In an 80 m long silica glass fiber, a small-signal pin of 39 dB has been achieved at a pump wavelength of 580 nm. The pin bandwidth is 127 cm-1 in small-signal amplification and 250 cm-1 in saturated amplification. In an 18 m long fluoride glass fiber, a small-signal gain of 9.3 dB has been obtained. The measured Raman-gain coefficient at 580 nm is (2 +/- 0.5) X 10(-11) cm/W in the fluoride glass fiber.