We study a class of nearest-neighbor discrete time integer random walks
introduced by Zerner (2005), the so called multi-excited random walks. The jump
probabilities for such random walker have a drift to the right whose intensity depends
on a random or non-random environment that also evolves in time according
to the last visited site. A complete description of the recurrence and transience
phases was given by Zerner (2005) under fairly general assumptions for the environment.
We contribute in this paper with some results that allows us to point
out if the random walker speed is strictly positive or not in the transient case for a
class of non-random environments.