  We study Friedmann--Robertson--Walker models with a perfect fluid matter
source and a scalar field nonminimally coupled to matter. We prove that a
general class of bounded from above potentials which fall to minus infinity as
the field goes to minus infinity, forces the Hubble function to diverge to
$-\infty$ in a finite time. This finite-time singularity theorem is true for
arbitrary coupling coefficient, provided that it is a bounded function of the
scalar field.
