This paper deals with an extension of the well‐known case of the harmonic oscillation of a nonkinked dislocation line to the case of both harmonic and anharmonic oscillations of a dislocation line in the presence of a moving kink. The one‐kinked dislocation is considered as the unbounded, nondissipative sine‐Gordon system, and the mixed, one‐soliton one‐periodic solutions of the sine‐Gordon equation, recently obtained by applying the method of Riemann theta function, are used for this purpose.