Abstarct: Although the standard model (SM) of electroweak interactions has had great predictions, there still remain some unanswered questions. Namely, no one can give a solid answer to the open question “which mechanism is responsible for the gauge symmetry breaking?”. Apart from the scalar dynamics of SM, many scenarios have been proposed to explain the nature of electro-weak symmetry breaking including the Higgs bosons of low-energy supersymmetry, little Higgs models, extra-dimensional theories of EWSB and strongly coupled EWSB sectors. In SM, however, the breaking of the SU U SU (2) (1) (3) × × symmetry is explained by the Higgs mechanism where one Higgs doublet is introduced. However, there exists no fundamental reason for the Higgs sector to contain only one Higgs doublet and multi-Higgs-doublets are acquired in many models, including supersymmetric models as well as models with spontaneous CP-breaking since introduction of a nonminimal Higgs sector can lead to new sources of CP violation in the Higgs sector and provides an attractive frxamework to study flavor changing processes as well. In the present thesis we first give a review on the two-Higgs-doublet model (2HDM) and then formulate a simple method to study positivity in NHDM with the general potential. Our approach can be used for a large class of Higgs triplets as well.