  Using a simplified pointwise iteration scheme, we establish nonlinear
phase-asymptotic orbital stability of large-amplitude Lax, undercompressive,
overcompressive, and mixed under--overcompressive type shock profiles of
strictly parabolic systems of conservation laws with respect to initial
perturbations $|u_0(x)|\le E_0 (1+|x|)^{-3/2}$ in $C^{0+\alpha}$, $E_0$
sufficiently small, under the necessary conditions of spectral and hyperbolic
stability together with transversality of the connecting profile. This
completes the program initiated by Zumbrun and Howard in \cite{ZH}, extending
to the general undercompressive case results obtained for Lax and
overcompressive shock profiles in \cite{SzX}, \cite{L}, \cite{ZH}, \cite{Z.2},
\cite{Ra}, \cite{MZ.1}--\cite{MZ.5}, and for special undercompressive profiles
in \cite{LZ.1}--\cite{LZ.2}, \cite{HZ}. In particular, together with spectral
results of \cite{Z.6}, our results yield nonlinear stability of large-amplitude
undercompressive phase-transitional profiles near equilibrium of Slemrod's
model \cite{Sl.5} for van der Waal gas dynamics or elasticity with
viscosity--capillarity.
