  We extend the strong macroscopic stability introduced in Bramson & Mountford
(2002) for one-dimensional asymmetric exclusion processes with finite range to
a large class of one-dimensional conservative attractive models (including
misanthrope process) for which we relax the requirement of finite range
kernels. A key motivation is extension of constructive hydrodynamics result of
Bahadoran et al. (2002, 2006, 2008) to nonfinite range kernels.
