  We consider dissipative dynamics of a flux qubit caused by 1/f noises, which
act both on the shunting LC-contour and on the SQUID loop. These classical
Gaussian noises modulate of the level splitting and of the tunnel coupling,
respectively, and they are partially correlated. The transient evolution of
qubit has been studied for the regimes: (a) the interwell incoherent tunneling,
(b) the relaxation of interlevel population, and (c) the decoherence of the
off-diagonal part of a density matrix. For all regimes, the relaxation rates
and the frequency renormalization [for the case (c)] are analyzed versus the
parameters of qubit and couplings to the noises applied. The fluctuation
effects give a dominant contribution at tails of relaxation, so that the
averaged dissipative dynamics is not valid there. The results obtained open a
way for verification of the parameters of qubit-noise interaction and for
minimization of coupling between qubit and environment. Under typical level of
noises, the results are comparable to the recent experimental data on the
population relaxation and on the incoherent interwell tunneling.
