We present a detailed mode identification performed on the 1994 Whole Earth Telescope (WET) run on GD 358. The results are compared with that obtained for the same star from the 1990 WET data. The two temporal spectra show very few qualitative differences, although amplitude changes are seen in most modes, including the disappearance of the mode identified as k 14 in the 1990 data. The excellent coverage and signal-to-noise ratio obtained during the 1994 run lead to the secure identification of combination frequencies up to fourth order, i.e. peaks that are sums or differences of up to four parent frequencies, including a virtually complete set of second-order frequencies, as expected from harmonic distortion. We show how the third-order frequencies are expected to affect the triplet q 2000 RAS

In each season when the DA pulsating white dwarf G29‐38 has been observed, its period spectrum appears very different, but it always contains a forest of harmonics and cross‐frequencies. The ratio of the amplitude of these non‐linear frequencies Ac to the product of the amplitudes of the corresponding parent modes A1A2 has been measured. The results are compared with the predictions given by three existing theoretical models. Our analysis shows that the non‐linear frequencies present in the period spectrum of G29‐38 owe their presence mostly to the inelastic response of the stellar medium to the perturbation travelling through it, rather than to the non‐linear response of the emergent luminous flux to the surface temperature variation. This analysis also confirms that most identified modes are ℓ=1, as previously asserted by Kleinman et al.

An analysis of the evolution of the amplitude spectrum over many seasons of the DA pulsating white dwarf G29‐38 has been performed. Neither beating nor resonant mode coupling can account for the observed appearance and disappearance of modes, although some of them clearly grow while others get damped. Therefore some unknown non‐adiabatic, non‐linear process has to be invoked that affects both the mode selection mechanism and the driving efficiency on a time‐scale as short as a day.

An analysis of the phase spectrum of the DA pulsating white dwarf G29‐38 over many seasons has been performed. This complements a companion paper which analyses the evolution of the temporal spectrum of G29‐38. We show that, with one exception, the relative phases of the harmonics and combination frequencies are all oscillating in phase with their parent modes. This not only suggests that these non‐linear frequencies owe their presence to harmonic distortion and not to resonant mode coupling, but also explains the typical pulse shapes observed in the light curves of large‐amplitude variable white dwarfs. The one exceptional cross‐frequency that does not show a phasing with its parent modes is thought to be a resonance.

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