A class of immigration superprocesses with dependent spatial motion for
deterministic immigration rate is considered,
and we discuss a convergence problem for the rescaled processes.
When the immigration rate converges to a non-vanishing deterministic one, then
we can prove that under a suitable scaling, 
the rescaled immigration superprocesses associated with
SDSM converge to a class of immigration superprocesses associated 
with coalescing spatial motion in the sense of probability distribution 
on the space of measure-valued continuous paths. 
This scaled limit not only provides with a new class of superprocesses 
but also gives a new type of limit theorem.