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A theory of travelling- and backward-wave variable parameter amplification appropriate to the amplification of a light beam is developed. It is an extension of the theory of Tien and Suhl for one-dimensional propagation to the case in which the pump wave, signal wave and idler waves have different directions of propagation. The theory is then applied to the design of a tuneable oscillator at optical wavelengths. The device is tuned by changing the orientation of a parallel mirror system. It appears that currently available pulsed laser powers are sufficient to drive such devices and that a continuous tuning range over a three to one interval in frequency is possible.