  Motivated by recent experiments with Josephson-junction circuits, we analyze
the influence of various noise sources on the dynamics of two-level systems at
optimal operation points where the linear coupling to low-frequency
fluctuations is suppressed. We study the decoherence due to nonlinear
(quadratic) coupling, focusing on the experimentally relevant 1/f and Ohmic
noise power spectra. For 1/f noise strong higher-order effects influence the
evolution.
