  In previous work on the Maxwell-Klein-Gordon system first existence and then
decay estimates have been shown. Here we show that the Maxwell-Klein-Gordon in
the Lorentz gauge satisfy the "weak null condition" and we give the detailed
asymptotics for the scalar field and the potential. These asymptotics have two
parts, one wave like along outgoing light cones at null infinity, and one
homogeneous inside the light cone at time like infinity. Here the charge plays
a crucial role in imposing an oscillating factor in the asymptotic system for
the field, and in the null asymptotics for the potential. Similar results have
previously been shown for Einstein's equations in wave coordinates, and the
Maxwell-Klein-Gordon system apart from being interesting in itself also
provides a simpler semilinear model of the quasilinear Enstein's equations.
