Summary: In [J. R. Christie and K. Gopalsamy, J. Aust. Math. Soc., Ser. B 37, No. 2, 186-207 (1995; Zbl 0853.34040)] the authors used Melnikov’s method to establish a sufficient condition for the existence of chaotic behaviour, in the sense of Smale, in a particular time-periodically perturbed planar autonomous system of ordinary differential equations. They concluded with an application to the dynamics of a one-dimensional anharmonic oscillator. The same system is considered and a condition for the existence of subharmonic orbits in the perturbed system is deduced, using the subharmonic Melnikov theory. Finally, an application is given to the dynamical behaviour of the one-dimensional anharmonic oscillator system.