  We show that a canonical, minimally coupled scalar field which is non-self
interacting and massless is equivalent to a null dust fluid (whether it is a
test or a gravitating field), in a spacetime region in which its gradient is
null. Under similar conditions, the gravitating and nonminimally coupled
Brans-Dicke-like scalar of scalar-tensor gravity, instead, cannot be
represented as a null dust unless its gradient is also a Killing vector field.
