  Most X-ray afterglows of gamma-ray bursts (GRBs) observed by the Swift
satellite have a shallow decay phase t^{-1/2} in the first few hours. This is
not predicted by the standard afterglow model and needs an explanation. We
discuss that the shallow decay requires an unreasonably high gamma-ray
efficiency, >75-90%, within current models, which is difficult to produce by
internal shocks. Such a crisis may be avoided if a weak relativistic explosion
occurs ~10^3-10^6 s prior to the main burst or if the microphysical parameter
of the electron energy increases during the shallow decay, \epsilon_e ~
t^{1/2}. The former explanation predicts a very long precursor, while both
prefer dim optical flashes from the reverse shock, as was recently reported. We
also calculate the multi-wavelength afterglows and compare them with
observations. No optical break at the end of the shallow X-ray decay indicates
a preference for the time-dependent microphysics model with additionally
decaying magnetic fields, \epsilon_B ~ t^{-0.6}.
