  We study the beahviour of the dual quark condensate $\Sigma_1$ in the
Nambu-Jona-Lasinio (NJL) model and its nonlocal variant. In quantum
chromodynamics $\Sigma_1$ can be realted to the breaking of the center symmetry
and is therefore an (approximate) order parameter of confinement. The
deconfinement transition is then signaled by a strong rise of $\Sigma_1$ as a
function of temperature. However, a similar behaviour is also seen in the NJL
model, which is known to have no confinement. Indeed, it was shown that in this
model the rise of $\Sigma_1$ is triggered by the chiral phase transition. In
order to shed more light on this issue, we calculate $\Sigma_1$ for several
variants of the NJL model, some of which have been suggested to be confining.
Switching between "confining" and "non-confining" models and parametrizations
we find no qualitative difference in the behaviour of $\Sigma_1$, namely, it
always rises in the region of the chiral phase transition. We conclude that
without having established a relation to the center symmetry in a given model,
$\Sigma_1$ should not blindly be regarded as an order parameter of confinement.
