  Class of exact solutions of the Skyrme and the Faddeev model are presented.
In contrast to previously found solutions, they are produced by the interplay
of the two terms in the Lagrangians of the models. They are not solitonic but
of wave character. With an appropriate choice of field variables, the field
equations of the two models are written in exactly the same form. The solutions
supply us with examples of the superposition of two plane waves in nonlinear
field theories.
