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A mathematical analysis is presented for dye laser amplifier chains used to amplify cw mode‐locked dye laser pulses up to the gigawatt regime. The model permits a discussion of the important aspects of the problem such as gain saturation, pulse shaping, and the optimization of pumping efficiencies. Experimentally, an amplifier chain has been demonstrated which is simple in design and operation without sacrificing high performance. A frequency doubled Q‐switched Nd:YAG oscillator alone is used to longitudinally pump three identical Brewster cells with the same flowing dye solution in each. The amplifier boosts the output of a synchronously mode‐locked dye laser to obtain ∼0.5 mJ≲1 psec pulses over a ∼400 Å bandwidth. These pulses are suitable for efficient Raman shifting, frequency mixing, and continuum generation to vastly extend the spectral range of the system. Some experimental results are presented to support the mathematical model.