In this study comprising a series of three articles, the model for pure CO₂ hydrate by Jäger et al. [Fluid Phase Equilib. 338 (2013) 100–113] has been improved and extended to other gases relevant in Carbon Capture and Storage (CCS) applications. The new model for eight pure gas hydrates is inspired by the currently most accurate model available for natural gas hydrates by Ballard and Sloan [Fluid Phase Equilib. 194 (2002) 371–383], which belongs to the family of van der Waals and Platteeuw (vdWP) models [Adv. Chem. Phys. 2 (1959) 1]. The new model is combined with highly accurate equations of state (EoS) in form of the Helmholtz energy for fluid phases and with Gibbs energy models for pure solid phases. Part I contains a critical analysis of the main parameters of the vdWP-based hydrate model. In this article (part II), the new hydrate model is described. A multi-property fitting algorithm is presented, which allows for simultaneous fitting of the model parameters to hydrate phase equilibrium data and to various types of hydrate composition data. Kihara potential parameters and reference parameters of the hydrate model were evaluated for eight selected hydrate formers; namely the CCS relevant gases carbon dioxide, argon, nitrogen, oxygen, carbon monoxide, and methane, and additionally ethane and propane. Experimental data used as an input to the fitting algorithm were weighted using uncertainty estimates. Estimation of the uncertainties of chemical potential along the three-phase coexistence lines including hydrates is a non-trivial task. Clearly, the uncertainty is dominated by various metastable and hysteresis effects, rather than by uncertainties of pressure and temperature measurements. For these reasons, some ad-hoc approaches have been developed. The uncertainty could straightforwardly be estimated in sparingly occurring regions covered by multiple data sources. Assuming a band of constant work of formation of hydrates along the three-phase coexistence lines then provided a plausible estimate of the uncertainties in a broad range of thermodynamic conditions. Usually, the Langmuir constant is fitted together with the reference state parameters of the hydrate model to three-phase hydrate formation data. In this work, a method is discussed that directly links the Langmuir constant to hydrate composition data. The performance of the new hydrate model dedicated to typical CCS gases in binary mixtures with water is demonstrated in part III. The model has been implemented in the software package TREND 2.0 by Span et al. [Thermodynamic Reference and Engineering Data 2.0. (2015) Lehrstuhl fuer Thermodynamik, Ruhr-Universitaet Bochum].