A theory is given for a new type of parametric amplifier which uses a gas discharge plasma as a nonlinear propagating medium. This theory is based on a zero‐temperature plasma assumption. The nonlinear coupling between traveling waves passing through the plasma is determined by taking second‐order terms in the velocity into account. A simplified normal mode theory is used to describe the effect on the propagation constants of the individual modes due to coupling between them. The theory is carried out in detail for a plasma in an infinite magnetic field and for a plasma in a zero magnetic field. The final propagation equation for the traveling waves is found in terms of the fields in the plasma of the small‐signal pumping wave, signal wave, and idler wave. In the Appendix the theory is extended to cover the case of beam‐type parametric amplifiers. It is shown that the theory is applicable both to beam‐type amplifiers which use space‐charge waves for all three modes of propagation or to waves which are partially those of a circuit and of the beam itself. The results obtained are in agreement with the theory of Louisell and Quate for the principal waves of a space‐charge wave parametric amplifier.