We present the results of our investigations of the dynamics of a classical hydrogen atom submitted to an intense classical radiation field with a relatively low frequency as compared to the characteristic Kepler frequency of the atomic system. We discuss here the harmonic spectra which can be deduced from a Fourier analysis of the time evolution of the strongly driven atomic dipole, associated either with a single trajectory or with ensembles of trajectories evolving from an initial microcanonical distribution. The spectra obtained from ensemble-averaged atomic dipoles qualitatively reproduce the main features of those recently observed in experiments and allow, in particular, discussion of the occurrence of a plateau in the distribution of harmonic intensities as a function of their order. The possible competition between harmonic generation and multiphoton ionization, which both take place in the same laser-intensity range, is also discussed.