Circadian clocks are internal timekeepers present in almost all organisms. Driven by a genetic network of highly conserved structure, they generate self-sustained oscillations that entrain to periodic external signals such as the 24 h light–dark cycle. Vertebrates possess multiple, functionally overlapping homologues of the core clock genes. Furthermore, vertebrate clocks entrain to a range of periods three times as narrow as that of other organisms. We asked whether genetic redundancies play a role in governing entrainment properties and analysed locomotor activity rhythms of genetically modified mice lacking one set of clock homologues. Exposing them to non-24 h light–dark cycles, we found that the mutant mice have a wider entrainment range than the wild types. Spectral analysis furthermore revealed nonlinear phenomena of periodically forced self-sustained oscillators for which the entrainment range relates inversely to oscillator amplitude. Using the forced oscillator model to explain the observed differences in entrainment range between mutant and wild-type mice, we sought to quantify the overall oscillator amplitude of their clocks from the activity rhythms and found that mutant mice have weaker circadian clocks than wild types. Our results suggest that genetic redundancy strengthens the circadian clock leading to a narrow entrainment range in vertebrates.