The EOSs for the quark matter in the unpaired or in the various colour superconducting phases employed in these investigations were obtained within the MIT bag model. Recently [40], a more realistic EOS for the unpaired quark matter computed within the NJL model is used to show that the maximum mass of the non-rotating hybrid stars depends sensitively on the choice of the EOS of the nuclear matter. It is necessary to construct stable configurations of the non-rotating and rotating hybrid stars using realistic EOSs for the nuclear matter and for the quark matter in the colour superconducting phases. In the present work, we compute several EOSs and use them to study the properties of the non- rotating and rotating hybrid stars composed of CSQM core. The lower density part of these EOSs correspond to the nuclear matter and are based on the variational and mean-field approaches. Our set of EOSs for the nuclear matter around the saturation density ( ρ$_{0}$ = 0 . 16 fm − $^{3}$) is constrained by the bulk properties of the finite nuclei. But, their behaviou r at densities, ρ > ρ$_{0}$ , are significantly di ff erent. The EOSs for CSQM are calculated within the NJL model using di ff erent values for the scalar diquark and vector current coupling strengths. The EOS at intermediate densities are obtained using a Maxwell construction. The paper is organized as follows, in Sec. II we describe , in brief, the models employed to construct the EOSs for nuclear matter and the CSQM. In Sec. III we present the results for the equilibrium sequences for non-rotating and rotating hybrid stars. In Sec. IV we state our conclusions. We compute the EOSs which correspond to the nuclear matter at lower densities and CSQM in the 2SC or CFL phases at higher densities. The EOS at intermediate densities are obtained using a Maxwell construction. For nuclear matter in the β equilibrium, we employ a set of diverse EOSs which are obtained using various approaches, like, variational, non-relativistic mean field (NRMF) and relativistic mean field (RMF). In Fig. 1 we plot various nu clear matter EOSs. The low density behaviour these EOSs are very much similar as they are constrained by the bulk properties of the finite nuclei. But, their behaviour at higher densities are s o di ff erent that the resulting neutron star properties are at variance. In Table I, we list some key properties of the non-rotating neutron stars obtained using these nuclear matter EOSs. It can be seen from Table I that the values of the maximum neutron star masses are in the range of 2 . 0 − 2 . 8 $^{M}$⊙ and the radius R$_{1}$$_{.}$$_{4}$ at the canonical 3 II. EQUATIONS OF STATE