Most models of new physics contain extended Higgs sectors with multiple Higgs bosons. The observation of an additional Higgs boson, besides the ∼ 125 GeV ‘hobs’, will thus serve as an irrefutable evidence of physics beyond the Standard Model (SM). However, even when fairly light, these additional Higgs bosons may still have escaped detection at the Large Electron-Positron (LEP) 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 GeV to about 150 GeV, in the Next-to-Minimal Supersymmetric SM (NMSSM) and the Type-I 2-Higgs Doublet Model (2HDM) in some such atypical search channels at the LHC Run-II.