  We investigate Non-Linear Plane-Wave solutions of the classical Minkowskian
Yang-Mills (YM) equations of motion. By imposing a suitable ansatz which solves
Gauss' law for the $SU(3)$ theory, we derive solutions which consist of Jacobi
elliptic functions depending on an enumerable set of elliptic modulus values.
The solutions represent periodic anharmonic plane waves which possess arbitrary
non-zero mass and are exact extrema of the non-linear YM action. Among them, a
unique harmonic plane wave with a non-trivial pattern in phase, spin and color
is identified. Similar solutions are present in the $SU(4)$ case while are
absent from the $SU(2)$ theory.
