  The long-time asymptotics is analyzed for all finite energy solutions to a
model U(1)-invariant nonlinear Klein-Gordon equation in one dimension, with the
nonlinearity concentrated at a point. Our main result is that each finite
energy solution converges as $t\to\pm\infty$ to the set of ``nonlinear
eigenfunctions'' $\psi(x)e\sp{-i\omega t}$.
