  Most models of new physics contain extended Higgs sectors with multiple Higgs
bosons. The observation of an additional Higgs boson, besides the $\sim 125$
GeV `$h_{\rm obs}$', will thus serve as an irrefutable evidence of physics
beyond the Standard Model (SM). However, even when fairly light, these
additional Higgs bosons may have escaped detection at the Large
Electron-Positron collider, the Tevatron and the Large Hadron Collider (LHC)
hitherto, owing to their highly reduced couplings to the SM particles.
Therefore, in addition to the searches based on the conventional production
processes of these Higgs bosons, such as gluon or vector boson fusion, possible
new search modes need to be exploited at collider experiments in order to
establish their signatures. We investigate here the phenomenology of
pseudoscalars, with masses ranging from $\mathcal{O}$(1) GeV to about 150 GeV,
in the Next-to-Minimal Supersymmetric SM and the Type-I 2-Higgs Doublet Model
in some such atypical search channels at the LHC Run-II.
