  A Neumann problem in the strip for the Fitzhugh Nagumo system is consid-
ered. The transformation in a non linear integral equation permits to deduce a
priori estimates for the solution. A complete asymptotic analysis shows that
for large t the effects of the initial data vanish while the effects of bound-
ary disturbances depend on the properties of the data. When they are convergent
for large t, the solution is everywhere bounded; when theirs first derivatives
belong to L one too, the effects are vanishing.
