  Compact microwave resonantors made of superconducting rings containing
Josephson junctions (SQUIDs) are attractive candidates for building frequency
tunable metamaterials with low losses and pronounced nonlinear properties. We
explore the nonlinearity of a SQUID metamaterial by performing a two-tone
resonant spectroscopy. The small-amplitude response of the metamaterial under
strong driving by a microwave pump tone is investigated experimentally and
theoretically. The transmission coefficient $S_{21}$ of a weak probe signal is
measured in the presence of the pump tone. Increasing the power of the pump, we
observe pronounced oscillations of the SQUID's resonance frequency
$f_{\textrm{res}}$. The shape of these oscillations varies significantly with
the frequency of the pump tone $f_{\textrm{dr}}$. The response to the probe
signal displays instabilities and sidebands. A state with strong second
harmonic generation is observed. We provide a theoretical analysis of these
observations, which is in good agreement with the experimental results.
