  In this paper we study global nonlinear stability for a system of semilinear
wave and Klein-Gordon equations with quadratic nonlinearities. We consider
nonlinearities of the type of wave-Klein-Gordon interactions where there are no
derivatives on the wave component. The initial data are assumed to have a
suitable polynomial decay at infinity, but are not necessarily compactly
supported. We prove small data global existence, sharp pointwise decay
estimates and linear scattering results for the solutions. We give a sufficient
condition which combines the Sobolev norms of the nonlinearities on flat time
slices outside the light cone and the norms of them on truncated hyperboloids
inside the light cone, for the linear scattering of the solutions.
