  We have studied the existence of traveling pulses in a general Type-I
excitable 1-dimensional medium. We have obtained the stability region and
characterized the different bifurcations behind either the destruction or loss
of stability of the pulses. In particular, some of the bifurcations delimiting
the stability region have been connected, using singular limits, with the two
different scenarios that mediated the Type-I local excitability, i.e.
homoclinic (saddle-loop) and Saddle-Node on the Invariant Circle bifurcations.
The existence of the traveling pulses has been linked, outside the stability
region, to a drift pitchfork instability of localized steady structures.
