  We analyze the long-time large-distance asymptotics of the longitudinal
correlation functions of the Heisenberg-Ising chain in the easy-axis regime. We
show that in this regime the leading asymptotics of the dynamical two-point
functions is entirely determined by the two-spinon contribution to their form
factor expansion. Its explicit form is obtained from a saddle-point analysis of
the corresponding double integral. It describes the propagation of a wave front
with velocity $v_{c_1}$ which is found to be the maximal possible group
velocity. Like in wave propagation in dispersive media the wave front is
preceded by a precursor running ahead with velocity $v_{c_2}$. As a special
case we obtain the explicit form of the asymptotics of the auto-correlation
function.
