  According to Popescu's recent analysis [Phys. Rev. Lett. {\bf72}, 797
(1994)], {\it nonideal} measurements, rather than ideal ones, may be more
sensitive to reveal nonlocal correlations between distant parts of composite
quantum systems. The outcome statistics of joint nonideal measurements on local
states should by definition admit local hidden variable models. We prove that
the density operator of a local composite system must be convex mixture of the
subsystems' density operators. This result depends essentially on a plausible
consistency condition restricting the class of admissible local hidden variable
models.
