This article focuses on the Goodwin oscillator and related minimal models, which describe negative feedback schemes that are of relevance for the circadian rhythms in Neurospora, Drosophila, and probably also in mammals. The temperature behavior of clock mutants in Neurospora crassa and Drosophila melanogaster are well described by the Goodwin model, at least on a semi-quantitative level. A similar semi-quantitative description has been found for Neurospora crassa phase response curves with respect to moderate temperature pulses, heat shock pulses, and pulses of cycloheximide. A characteristic feature in the Goodwin and related models is that degradation of clock-mRNA and clock protein species plays an important role in the control of the oscillator's period. As predicted by this feature, recent experimental results from Neurospora crassa indicate that the clock (FRQ) protein of the long period mutant frq7 is degraded approximately twice as slow as the corresponding wild-type protein. Quantitative RT-PCR indicates that experimental frq7-mRNA concentrations are significantly higher than wild-type levels. The latter findings cannot be modeled by the Goodwin oscillator. Therefore, a threshold inhibition mechanism of transcription is proposed.