  We consider a class of wave-Schroedinger systems with a Zakharov-Schulman
type coupling. This class of systems is indexed by a parameter gamma which
measures the strength of the null form in the nonlinearity of the wave
equation. The case gamma = 1 corresponds to the well-known Zakharov system,
while the case gamma = -1 corresponds to the Yukawa system. Here we show that
sufficiently smooth and localized Cauchy data lead to pointwise decaying global
solutions which scatter, for any gamma in (0,1].
