The influence of global inhibition on travelling pulses both in infini
te and in finite periodic systems is investigated. Analytic investigat
ion of the modified piecewise linear Rinzel-Keller-Model (RKM) shows a
shrinking and slowing down of pulses due to global inhibition. Analyt
ic results obtained are confirmed by numerical simulations. The invest
igation is completed by numerical simulations of the modified Oregonat
or model for the light-sensitive BZR.