  We show that $1/f$-noise in the variable range hopping regime is related to
transitions of many-electrons clusters (fluctuators) between two almost
degenerate states. Giant fluctuation times necessary for $1/f$-noise are
provided by slow rate of simultaneous tunneling of many localized electrons and
by large activation barriers for their consecutive rearrangements. The Hooge
constant steeply grows with decreasing temperature because it is easier to find
a slow fluctuator at lower temperatures. Our conclusions qualitatively agree
with the low temperature observations of $1/f$-noise in p-type silicon and
GaAs.
