  There are three basic processes that determine hopping transport: (a) hopping
between normally empty sites (i.e. having exponentially small occupation
numbers at equilibrium); (b) hopping between normally occupied sites, and (c)
transitions between normally occupied and unoccupied sites. In conventional
theories all these processes are considered Markovian and the correlations of
occupation numbers of different sites are believed to be small(i.e. not
exponential in temperature). We show that, contrary to this belief, memory
effects suppress the processes of type (c), and manifest themselves in a
subleading {\em exponential} temperature dependence of the variable range
hopping conductivity. This temperature dependence originates from the property
that sites of type (a) and (b) form two independent resistor networks that are
weakly coupled to each other by processes of type (c). This leads to a
two-color percolation problem which we solve in the critical region.
