A mathematical treatment is given of the wave phenomena in a traveling wave parametric amplifier. The waves are described by two coupled differential equations of the 2nd order. By the elimination of one of the unknowns a 4th order differential equation arises. There are 4 waves of the signal frequency and 4 waves of the idler frequency, in contrast to linear transmission lines, where there are only 2 waves on a single frequency. The influence of the reflected waves on the stability of the amplifier is investigated, and oscillation criteria are given. Some methods to prevent oscillation are suggested. (Author.