  We consider a variation of the Generalized Excited Random Walk (GERW) in
dimension $d\ge 2$ where the lower bound on the drift for excited jumps is
time-dependent and decays to zero. We show that if the lower bound decays
slower that $n^{-\beta}$ ($n$ is time), for $\beta$ depending on the
transitions of the process, the GERW is transient in the direction of the
drift.
