  We formulate and prove a new criterion for stability of e-processes. It says
that any e-process which is averagely bounded and concentrating is
asymptotically stable. In the second part, we show how this general result
applies to some shell models (the Goy and the Sabra model). Indeed, we manage
to prove that the processes corresponding to these models satisfy the e-process
property. They are also averagely bounded and concentrating. Consequently,
their stability follows.
