  We study the connection of the chiral dynamics in QED and QCD in a strong
magnetic field with noncommutative field theories (NCFT). It is shown that
these dynamics determine complicated nonlocal NCFT. In particular, although the
interaction vertices for electrically neutral composites in these gauge models
can be represented in the space with noncommutative spatial coordinates, there
is no field transformation that could put the vertices in the conventional form
considered in the literature. It is unlike the Nambu-Jona-Lasinio (NJL) model
in a magnetic field where such a field transformation can be found, with a cost
of introducing an exponentially damping form factor in field propagators. The
crucial distinction between these two types of models is in the characters of
their interactions, being short-range in the NJL-like models and long-range in
gauge theories. The relevance of the NCFT connected with the gauge models for
the description of the quantum Hall effect in condensed matter systems with
long-range interactions is briefly discussed.
