  We study the relaxation modes of an interface between a lyotropic lamellar
phase and a gas or a simple liquid. The response is found to be qualitatively
different from those of both simple liquids and single-component smectic-A
liquid crystals. At low rates it is governed by a non-inertial, diffusive mode
whose decay rate increases quadratically with wavenumber, $|\omega|=Aq^2$. The
coefficient $A$ depends on the restoring forces of surface tension,
compressibility and bending, while the dissipation is dominated by the
so-called slip mechanism, i.e, relative motion of the two components of the
phase parallel to the lamellae. This surface mode has a large penetration depth
which, for sterically stabilised phases, is of order $(dq^2)^{-1}$, where $d$
is the microscopic lamellar spacing.
