able corrections in two different ways and hence are referred as QPM I and QPM II in the following. Moreover, these descriptions were initially given for the gluon plasma only. We extend both the models for a QGP with finite baryon chemical potential µ$_{B}$ and we further assume their validity starting from a threshold temperature T$_{0}$ = 100 MeV below the crit- ical temperature T$_{c}$ and we adjust the parameters of the models accordingly. We further compare their predictions for the energy density ϵ and the pressure p of the QGP with those obtained previously from the lattice simulation approach. Furthermore, we obtain a new EOS for the hot and dense HG as formulated in the previous paper and construct the phase boundary by equating the QGP pressure with that of HG pressure.We thus determine the critical parameters in the Gibbs’ construction of a first order deconfining phase transition. We draw the phase boundary line and the end of the line determines the coordinates of the CEP. We also find the existence of a crossover transition lying beyond CEP. Finally we compare our findings with those obtained in various other models. The plan of the paper runs as follows. There are two types of quasiparticle models which are thermodynamically self consistent. In section II, we describe quasiparticles (QP), their corresponding equation of state and discuss the criterion of thermodynamical consistency. In section III, we describe the first thermodynamically consistent quasiparticle model [15] of Gorenstein and Yang, the dependence of the quark and gluon masses on the temperature and the extension of the model to describe the physics at finite µ$_{B}$ . In section IV, we discuss the second thermodynamically consistent quasiparticle model [16] of Bannur and its exten- sion for the finite µ$_{B}$ . In section V, we give our formulation for an excluded volume model for the hot and dense hadron gas, and we discuss about its thermodynamical consistency. Section VI summarizes our results and discussions. Quasiparticles are the thermal excitations of the interacting quarks and gluons.The quasi- particle model in QCD is a phenomenological model which is widely used to describe the non-ideal bahaviour of QGP near the phase transition points. It was first proposed by Golviznin and Satz [17] and then by Peshier et. al. [18] to explain the EOS of QGP obtained from lattice gauge simulation of QCD at finite temperature. In quasiparticle mod- els, the system of interacting massless quarks and gluons can be effectively described as II. QUASIPARTICLE MODELS (QPM)