  In this paper we briefly review the LHC discovery potential of a light
pseudoscalar Higgs boson of the NMSSM, $a_1$, produced in the gluon fusion
$gg\to a_1$ , bottom-quark fusion $b\bar b\to a_1$ and bottom-gluon fusion
$bg\to ba_1$. We also review the LHC discovery potential of the
next-to-lightest CP-even Higgs boson $h_2$ being the non-SM-like Higgs,
decaying either into two light CP-odd Higgs bosons $a_1 a_1$ or into a light
$a_1$ and the $Z$ gauge boson through the gluon fusion $gg \to h_2$ in the
4$\tau$ final state. We find that the light $a_1$ can be detected at the LHC in
a variety of production processes including the gluon fusion, bottom-quark
fusion and bottom-gluon fusion. The latter two processes require high
luminosity of the LHC and large values of tan$\beta$. We also find that the LHC
has the potential to discover the non-SM-like Higgs state, $h_2$, decaying into
a pair of light CP-odd Higgses $a_1$'s, allowing to distinguish the NMSSM Higgs
sector from the MSSM one as such a light $a_1$ is impossible in the latter
scenario.
